Mixed Speed, Distance, Time Questions - Lesmahagow … · Web viewA car, starting from rest, reaches a speed of 15 metres per second in a time of 30 seconds. Calculate the acceleration

Dynamics and SpaceQuestion Booklet 1

Dynamics

Physics

Speed Distance Time Questions

1. Calculate how far a car travels in 300 seconds when it is travelling at a top speed of 30 m/s.

2. How long does it take to walk to school if you walk at an average speed of 3 m/s and you live 900 metres away?

3. Find the average speed of a motor boat which takes 350 seconds to cover a 10 000 m course.

4. A runner takes 35 seconds to run round 250 metres of a track. What is his average speed?

5. A train travelling at 35 m/s takes 15 seconds to pass through a tunnel. How long is the tunnel?

6. Find the average speed of Sammy Snail who slithers 0005 m in 4 seconds.

7. How long does the TGV take to travel 60 000 m given that it goes at an average speed of 30 m/s.

8. A school bus takes 20 minutes to travel 15 km. What is it’s average speed? (Give your answer in m/s)

9. A bird maintains an average speed of 112 m/s for 5 minutes. How far does it travel?

10. How long does a roller blader take to travel 2km if his average speed is 7 m/s?

Dynamics and Space 2©GMV Science. Photocopiable only by the purchasing institution

1. Rounding answers off.When using your calculator, answers often work out to have more than one number after the decimal point.It is usual to round off the answer you see on the display to two numbers after the decimal point, unless stated otherwise.

Practise rounding answers off to two numbers after the decimal point by doing the following calculator exercises.(a) 2 18 (b) 3 9 (c) 40 82 (d) 23.592

(e) 625 x 421 (f) 361 x 654 (g) 798 x 1324(h) 276 x 113

2. Using the button/ button/ button or button is one of the most useful function buttons on

your calculator. It allows you to handle very small and very large numbers easily.

or means ‘times ten to the power of’

So, 3 x 108 can be entered into the calculator as 3 8 or 3 8

(Note: there is no need to enter ‘x’ before either function button.)

3 x 10-8 can be entered into the calculator as 3 8 or 3 8

Try entering the following numbers in scientific form into your calculator and write down what you see on the display. (Use either the or the function button depending on the model of calculator you have.)

(a) 3 x 108 (b) 14 x 106 (c) 34 x102

(d) 106 x 104 (e) 999 x 109 (f) 567 x 105

(g) 3 x 10-8 (h) 14 x 10-6 (i) 34 x 10-2

(j) 106 x 10-4 (k) 999 x 10-9 (l) 567 x 10-5


EXP

EXP

EXP

EXP EXP

EXP

+/ - +/

-

EE X10x

X10x

X10x

X10x

X10x

X10x

Calculator Exercises3. PracticeA display like 3 08 really means 3 x 108 and 4 -06 really means 4 x 10-6

which may seem strange since the ‘x 10’ does not appear.Try the following calculator exercises and write down the answers. Remember to add in the ‘x 10’ part yourself, don’t just copy down what you see on the display.

(a) 3 x 105 x 5 x 107 (b) 46 x 109 x 778 x 1026

(c) 456 x 1045 x 5 x 105 (d) 06 x 1010 x 02 x 1010

(e) 498 x 1021 323 x 103 (f) 999 x 103 888 x 101

(g) 20 x 10-9 x 34 x 10-3 (h) 345 x 10-2 x 399 x 10-5

(i) 056 x 10-4 x 323 x 10 -3 (j) 144 x 10-7 x 777 x 10-4

(k) 666 x 10-66 777 x 10-2 (l) 5 x 10-3 6 x 10-6

(m) 345 x 10-6 x 567 x 109 (n) 767 x 1012 32 x 10-9


EXP

average speed

distance time=

= d t

Average SpeedIn this section you can use the equation:

also written as

Where v= average speed in metres per second (m/s)d= distance in metres (m)t= time in seconds (s).

(f) Find the missing values in the following table.Average speed

(m/s)Distance (m) Time (s)

(a) 100 20

(b) 20 4

(c) 25 0·5

(d) 16 55

(e) 1·2 x 103 60

(f) 75 1·5 x 104

2. A car travels a distance of 2 000 metres in a time of 160 seconds. Calculate the average speed of the car in metres per second.

3 Jane jogs to work every day at an average speed of 4 m/s. Most days it takes her 600 seconds to reach work. Calculate how far she jogs.

4. A model train travels round 10 m of track at an average speed of 1·5 m/s. How long does this take?

Dynamics and Space 5

©GMV Science. Photocopiable only by the purchasing institution

Average Speed5. Christopher takes 26 seconds to swim one length of a swimming pool. If

the pool is 50 metres long calculate his average speed.

6. How far will a cyclist travel in 60 seconds if he is travelling at an average speed of 13 m/s ?

7. Calculate a hurdler’s time if she completes the 400 m hurdle race at an average speed of 7 m/s.

8. How far will a jet aircraft travel in 5 minutes if it flies at 400 metres per second?

9. The Channel Tunnel is approximately 50 km long. How long will it take a train travelling at 90 m/s to travel from one end of the tunnel to the other?

10. A hill walker walks at an average speed of 1·6 m/s. How long will it take her to cover a distance of 33 km?

11. A lorry takes 4 hours to travel 150 km. Calculate the average speed of the lorry in m/s.

12. Richard Noble captured the world land speed record in 1983 in his vehicle Thrust 2. The car travelled one km in 3·5 seconds. Calculate the average speed of the car.



Average Speed13. The table below shows part of a timetable for the Glasgow to Aberdeen

train

Station Departure time Distance (km)Glasgow 1025 0

Perth 1125 100Dundee 1148 142

Aberdeen 1324 250

(a) Calculate the average speed of the train in m/s over the whole journey.

(b) Between which stations is the train’s average speed greatest?

14. The Wright brothers were the first people to fly an aeroplane. Their first flight in 1903 lasted only 12 seconds and covered just 36 metres.

(a) Calculate the average speed of the plane during that first journey.

(b) Today a Tornado fighter jet can fly at Mach 2 (twice the speed of sound). How long would it take the jet to travel 36 metres?

(Speed of sound in air = 340 m/s)



Average Speed15. A long distance lorry driver has 3 hours to travel 210 km to catch the

Northlink ferry.

b) Calculate the average speed at which the lorry must travel in order to reach the ferry on time. Give your answer in km/h.

c) Due to heavy traffic the lorry has an average speed of 60 km/h for the first 100 km. Calculate how long this leg of the journey takes.

d) At what speed must the lorry travel for the rest of the journey if the driver is to catch the ferry? Give your answer in km/h.

16. The cheetah is the fastest mammal on earth. It can run at an average speed of 40 m/s but can only maintain this speed for short periods of time. Cheetahs prey on antelopes. The average speed of an antelope is 35 m/s. The antelope can maintain this speed for several minutes.

a) Calculate how far a cheetah could run in 12 seconds if it maintained an average speed of 40 m/s.

b) How long would it take an antelope to run 480 m?

c) A cheetah is 80 m away from an antelope when it begins to chase it.The antelope sees the cheetah and starts to run at the same instant

that the cheetah begins its chase. Both animals run at their average speeds and the cheetah is able to run for 15 s. Show by calculation whether or not the cheetah catches the antelope.



Average Speed17. Before a major motor race the competitors complete practice circuits in

their cars. These practice runs are timed and used to determine the position of each car at the starting grid for the race. The race circuit is 3·6 km long.

In a particular race each driver completed four practice laps. The practice lap times for the top three drivers are shown in the table.

Driver Name

Lap Times

(s)

1 2 3 4Mickey 45·8 43·4 46·4 48·2Donald 44·7 46·2 44·6 49·5Goofy 46·3 44·8 45·1 43·8

a) Which driver had the greatest average speed during lap 1?

b) Calculate the greatest average speed during lap 2.

c) For each driver calculate their average speed in metres per second for the complete practice run.

d) Which driver is most likely to win the race?



vi =

dt

instantaneous speed

width of masktime to cut beam

=

Instantaneous SpeedIn this section you can use the idea that:

instantaneous speed = average speed over as short a time as possible

also written as

where vi = instantaneous speed in metres per second (m/s)d = distance in metres (m)t = time in seconds (s).

(1)The following experiment is used for measuring the instantaneous speed of a trolley as it travels down a runway.

Use the equation

to find the missing values in the following table:

instantaneous speed (m/s)

mask length (m)

time (s)

(a) 0·02 0·1(b) 0·015 0·1 (c) 4·1 0·03(d) 3·5 0·05(e) 2·0 0·2(f) 1·86 0·01



0·05 s

Instantaneous Speed2. An observer wants to find the instantaneous speed of a car as it passes a

pedestrian crossing. He measures the length of the car and finds it to be 3·5 m. He then stands with a stop watch at the crossing, starts timing as the front of the car passes him and stops when the back of the car has passed. The time recorded is 2·4 s.Calculate the instantaneous speed of the car.

3. A runner decides to analyse his track performance in order to improve his overall running time during the 400 m event. He sets up light gates at six points round the track so that he can work out his instantaneous speeds at each point.As the runner cuts the beam of light from the light gate the timer operates.

The results he recorded are shown below.Position width of runner (m) time

(s)instantaneous speed (m/s)

A 0·2 0·025B 0·2 0·026C 0·2 0·030D 0·2 0·029E 0·2 0·025F 0·2 0·024

Use the results to calculate his instantaneous speed at each position and hence say at which point is he running:

(a) fastest(b) slowest?



instantaneous speed

width of runner runnertime to cut beam

=

Instantaneous Speed4. Civil engineers need to know the speeds of a train as it enters a tunnel

which they are planning to build. They set up their equipment to measure the length of a section of the train and time how long that section takes to pass the planned point of entry to the tunnel.The length of train is 150 m and the time to pass the point of entry is recorded as 1·42 s. Calculate the instantaneous speed of the train.

1.2.3.4.5. A coin is dropped from a height so that it passes through a light gate

connected to a computer. The coin has a width of 0·02 m and it takes 0·005 seconds to pass through the light gate. Find its instantaneous speed.



Mixed Speed, Distance, Time QuestionsSpeed, distance and time

1. A runner completes a 200 m race in 25 s. What is his average speed in m/s?

2. A friend asks you to measure his average cycling speed along flat road. Describe which measurements you would take and the measuring instruments you would use.

3. An athlete takes 4 minutes 20 s to complete a 1500 m race. What is the average speed?

4. On a fun run, a competitor runs 10 km in 1 hour. What is her average speed in

a. km/hb. m/s?

5. Describe how you could measure the average speed of a car as it passes along the road outside your school/college.

6. Concorde can travel at 680 m/s (twice the speed of sound). How far will it travel in 25 s at this speed?

7. A girl can walk at an average speed of 2 m/s. How far will she walk in 20 minutes?

8. How long will it take a cyclist to travel 40 km at an average speed of 5 m/s?

9. How long (to the nearest minute) will the Glasgow to London shuttle take if it flies at an average speed of 220 m/s for the 750 km flight?

10. How long, to the nearest minute, will a car take to travel 50 km if its average speed is 20 m/s?


Physics: Mechanics and Heat (Int2) – Student Material

Mixed Speed, Distance, Time Questions11. Look at this timetable for a train between Edinburgh and Glasgow:

Station Time Distance from Glasgow

Glasgow 0800 0 km Falkirk 0820 34 kmLinlithgow 0828 46 kmEdinburgh 0850 73 km

a) What was the average speed for the whole journey in m/s?b) What was the average speed in m/s between Glasgow and

Falkirk?c) Explain the difference in average speeds in a) and b).

12. Describe how you would measure the instantaneous speed of a vehicle as it reached the bottom of a slope.

13. In an experiment to measure instantaneous speed, these measurements were obtained:-

Reading on timer = 0.125 sLength of car = 5 cm

Calculate the instantaneous speed of the vehicle in m/s.

14. A trolley with a 10 cm card attached to it is released from A and runs down the slope, passing through a light gate at B, and stopping at C.Time from A to B = 0.8 s.Time on light gate timer = 0.067 s

a) What is the average speed between A and B?b) What is the instantaneous speed at B?



time in s

BSpeed Time Graphs

1. L o o k a t e a c h o f t h e s p e e d t i m e g r a p h s d r a w n b e l o w a n d d e s c r i b e t h e

motion of the vehicle.(a) (b) (c)

2. Draw speed time graphs to represent each of the following journeys.(a)

time (s) 0 2 4 6 8 10 12speed (m/s) 0 5 10 15 15 15 0

(b)time (s) 0 1 2 3 4 5 6

speed (m/s) 0 20 40 30 30 10 0(c)

time (s) 0 10 20 30 40 50 60speed (m/s) 50 40 30 20 10 60 0



speedin m/s AB: car accelerates from rest

BC: car travels at a constant speed

00 0

A B

C

speedin m/s

time in sA

BD

Cspeedin m/s

time in s B

A

E

D

C

speedin m/s

time in s

Speed time graphs can be used to describe the motion of a vehicle.

time in s10

speedin m/s

2

5

0

speedin m/s

time in s10 18

50

0

speedin m/s

time in s

30

120speedin m/s

time in s

25

5

200

speedin m/s

20

time in s 14

10

320

30

time in s3012

0

5

time in s

speedin m/s

42

21

18 280time in s

speedin m/s

100

10 35 550

time in s

20speedin m/s

5

16 240

Using Speed Time Graphs to Calculate Distance

1. Use the speed time graphs below to calculate the distance travelled during each journey.

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

2. While driving along a motorway a driver spots an accident and brakes. The speed time graph below represents the motion of the car from the instant the driver sees the accident.

25speed 20



5

Helpful Hint

To work out how far an object has travelled when it is accelerating or decelerating you must use:

distance travelled = area under speed time graph

Remember!You cannot use:distance = speed x time.

This is only for objects travelling at a constant speed.

Using Speed Time Graphs to Calculate Distancein m/s 15

10 5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 time in s

(a) When did the driver brake?(b) Calculate how far the car travelled before braking.(c) Calculate how far the car travelled after the driver braked.

3. Draw a speed time graph to represent the following motion recorded for a train leaving a station.

Time (s) 0 10 20 30 40 50 60 70 80 90speed

(m/s)0 5 10 15 20 25 25 25 30 30

Use the graph to calculate:(a) describe the motion of the train during the 90 seconds(b) the distance travelled by the train in 90 seconds.

4. Draw a speed time graph to represent the following motion recorded as a car approaches traffic lights.

Use the graph to calculate:

(a) describe the motion of the car during the 90 seconds.(b) the distance travelled by the car in 90 seconds



Time (s) 0 10 20 30 40 50 60 70 80 90speed

(m/s)20 20 20 15 15 10 10 5 5 0

80604020

0

Using Speed Time Graphs to Calculate Distance5. A hang glider is cruising over choppy waters at a speed of 15 m/s when

the wind direction suddenly changes and sends him into a deep dive increasing his speed.

25speed 20in m/s 15

10 5 0 2 4 6 8 10 12 14 16 18 20 22 24 time in s

Use the speed time graph shown to:(a) state when the dive started(b) calculate how far he travelled during the dive.

6. The motion of a rocket as it approaches the moon is shown below.

Speed in m/s

0 2 4 6 8 10 12 14 16 18 20 22 24 26 time

in s

(a) Calculate the distance the rocket travelled during the time it was accelerating.

(b) Does the rocket actually reach the moon’s surface if it is 580 metres above it when its deceleration begins? You must justify your answer.



0 2 4 6 8 10 12 14 16 18 20 22 time in s

Using Speed Time Graphs to Calculate Distance7. Part of a bus journey is represented by the speed time graph below.

speed 10 in m/s 8 6 4 2

Use the graph to calculate :(a) describe the motion of the bus during the 22 seconds(b) the total distance travelled by the bus(c) the average speed of the bus.



Vectors and Scalars 11. State the difference between a vector and a scalar quantity.

2. Arrange the following quantities into a table with the headings Vectors and Scalars

time, speed, displacement, distance, velocity, acceleration, force, mass, weight, energy.

3. Find the resultant displacement of the two distances shown (use scale drawing).

4. A runner runs on the perimeter of a square field as shown on the right. He starts at A and runs to C.

(a) What distance has the runner travelled when he reaches C ?

(b) Calculate the runner’s displacement on reaching C (magnitude and direction).

5. A car travels 4km east and then 9km north. Calculatea) The distance travelled by the carb) The displacement of the car.

6. A runner follows the path shown starting at A and arriving at B ten seconds later.

a) What is the distance travelled by the runner?b) Calculate the average speed of the runner.c) Calculate the runner’s displacement

(magnitude and direction).d) Calculate the average velocity of the runner

(magnitude and direction).


SIC Physics Development Group MS CMG

Vectors and Scalars 17. During a boat race, a yacht sails the course shown in Figure 1.

(a) What is the total distance travelled by the yacht in moving from O to B?

(b) Calculate, by scale diagram or otherwise the magnitude and direction of the displacement from O of the yacht on reaching B.

The yacht takes 15 minutes to reach point B, from point O.

(c) What is the average speed of the yacht during this part of the race?

(d) Calculate the average velocity of the yacht when moving from O to B.

8. A polar bear walks 7km due North and then 6km due West.The complete journey takes the polar bear 2.5 hours.Find:

a) the total distance travelled by the polar bear (in km)b) the polar bear’s average speed (in km/h)c) the total displacement of the polar beard) the polar bear’s average velocity

9. An orienteer ran 6 km North and then 8 km East. He ran on level ground and it took him 2 hours.

(a) Calculate his average speed in km/h(b) Calculate his average velocity (give magnitude and direction).

10. A man walks 50m north, 40m east and 30m south.a) What distance did he walk b) What is his resultant displacement?

If he took 60s to do this find(c) his average speed (d) his average velocity

11. A boat has a speed of 8 m/s and aims north to cross a river at. The current is running at 6 m/s to the east. The crossing takes 20s.

a) Find the resultant velocity of the boat. b) How far down the opposite bank does the boat land compared

toDynamics and Space 21


Vectors and Scalars 1 the point opposite its starting position?

12. An aircraft flies with velocity 130 m/s due north. A cross wind is blowing to the West at 15m/s. Calculate the resultant velocity of the aircraft.

13. The crew of a rowing boat attempt to row directly east across Bressay Sound. The crew can row in still water at a speed of 6 knots, but a tide is running north at 2 knots.

(a)Draw a diagram(b)Calculate the actual velocity of the rowing boat.

1.2.3.4.5.6.7.8.9.10.11.12.13.14. A hovercraft travels between two ports, one directly to the north

of the other. The hovercraft’s cruising speed in still conditions is 40 m/s. A steady, strong wind blows from the east at 20 m/s. In what direction (3 figure bearing) must the hovercraft point its bow in order to travel directly northwards? (Hint: you know one thing about the resultant now!)



Vectors and Scalars 21. What is the difference between a vector quantity and a scalar

quantity?

2. Use your answer to question 1 to explain the difference between distance and displacement.

3. A man walks from X to Y along a winding road.

a) What is his displacement at the end of his walk?b) What distance has he walked?

4. If the walker in question 3 took 40 minutes for his walk, what wasa) his average speedb) his average velocity?

5. One complete lap of a running track is 400m. An athlete completes one lap in

48 s in the 400 m race. What is his

a) distance travelledb) displacementc) average speedd) average velocity.

6. Repeat Q 5 for a runner in the 800 m race whose winning time was 1 min 54 s.

7. A car travels 40 km north, then turns back south for 10 km. The journey takes 1 hour. What is



Vectors and Scalars 2 a) the displacement of the carb) the distance the car has travelledc) the average velocity of the car (give answer in km/h)d) the average speed of the car? (give answer in km/h)

8. A car drives 60 km north, then 80 km east, as shown in the diagram. The journey takes 2 hours.Calculate the

a) distance travelledb) displacementc) average speedd) average velocity.



Velocity Time Graphs1. The graph below shows how the velocity of a car varies over a 40 s

period.

a) Describe the motion of the car during this 40 s period.b) Calculate the acceleration of the vehicle.c) How far does the car travel while accelerating?d) What is the total distance travelled by the car?

2. Use the graph below to answer the following questions.

a) During which time is the vehicle travelling at a constant velocity?b) Calculate the values of i) the initial acceleration ii) the final

decelerationc) What is the braking distance of the car?d) What is the total distance travelled?e) What is the average velocity of the car?

3. Draw a velocity-time graph to describe the following motion:-A car accelerates from rest at 2 m/s2 for 8 s, then travels at a constant velocity for 12 s, finally slowing steadily to a halt in 4 s.

4. For the vehicle in the previous question, what are the values ofa) the maximum velocityb) the distance travelledc) the average velocity?

5. The graph below describes the motion of a cyclist.



0

Velocity Time Graphs

a) What is the value of the maximum positive acceleration?b) Show by calculation whether the cyclist travels farther while

accelerating, or while cycling at the maximum velocity.



0

Acceleration 1In this section you can use the equation:

also written as

where a = acceleration in metres per second per second (m/s2)u = initial speed in metres per second (m/s)v = final speed in metres per second (m/s)t = time taken for change in speed in seconds (s).

1. Find the missing values in the following table .Acceleration

(m/s2)Change in Speed

(m/s)Time taken

(s)

(a) 12 6

(b) 20 5

€ 0·05 180

(d) 0·4 600

€ 3 12

(f) 5 45

2. A car, starting from rest, reaches a speed of 15 metres per second in a time of 30 seconds. Calculate the acceleration of the car.

3. A sprinter in a race crossed the finishing line with a speed of 14 m/s. If her sprint time was 16 seconds, what was her average acceleration?



acceleration = change in speedtime taken

a = v - u t

Acceleration 14. A ball is dropped from the roof of a building. What is the acceleration of

the ball if its speed is 30 m/s after 3 seconds?

5. What is the acceleration of a lorry which increases its speed from 5 m/s to 15 m/s in 40 seconds?

6. A train increases its speed from 15 m/s to 25 m/s in a time of 8 seconds. Calculate the acceleration of the train.

7. A train, which had been travelling at 18 m/s, took 12 seconds to stop from the moment the brakes were applied. What was the deceleration of the train?

8. A bus, travelling at 16 m/s, takes 32 seconds to come to rest. Calculate the deceleration of the bus.

2.3.4.5.6.7.8.9. What is the deceleration of a car which slows down from 10 m/s to 4

m/s in 8 seconds?

10. It takes 20 seconds for an ice skater to come to rest after skating with a speed of 8 m/s. What is her deceleration?

11. A hot air balloon was ascending at a constant speed. It then accelerated at 0·08 m/s2 for 1 minute. If it reached a speed of 5 m/s, what was its speed before the acceleration?



Acceleration 1

12. A train is accelerating at a rate of 1·2 m/s2.. How long will it take for the speed of the train to increase from 5 m/s to 16·4 m/s?

13. A boy is cycling on a flat road with a speed of 12 m/s when he stops edaling. He decelerates at a rate of 0·4 m/s2. How long does he take to stop?

14. A hot air balloon accelerates upwards from the ground at 0·05 m/s2. It maintains this acceleration for the first 40 seconds of its flight. One sandbag is then released which increases the acceleration of the balloon to 0·08 m/s2.

(a) What is the speed of the balloon 40 seconds after it has been released from the ground?

(b) What is the speed of the balloon 20 seconds after the sandbag is released?

2.3.4.5.6.7.8.9.10.11.12.13.14.15. A car accelerates at a rate of 0·3 m/s2 for 15 seconds and

reaches a speed of 18 m/s. What was its original speed?

16. A bus travelling at a constant speed decelerates at 0·8 m/s2 for 4 s. If its speed drops to 12 m/s, what was the original speed of the bus?



Acceleration 21. Describe in words what we mean by the acceleration of an object.

2. Explain what is meant by an acceleration of 4m/s2.

3. A vehicle starting from rest accelerates at a steady rate of 6m/s2 along a level road. How fast will it be travelling after:

a. 2s b. 3s c. 5s d. 9s

4. A bus accelerates uniformly from 8 m/s to 16 m/s in 4s.

Find the acceleration.

5. A car travelling at 27m/s crashes into a wall and comes to rest in 1.2s. Calculate the acceleration.

6. A tennis ball is dropped from a bridge accelerates to 4.9 m/s in 0.5s.

a) Calculate the acceleration due to gravity showing all working clearly.

b) Suggest one a method for timing the ball.

7. A pupil is investigating the acceleration of a trolley running down a slope.

They have the following apparatus:2 light gates, an electronic timer, a metre stick, stopwatch and card.Describe with aid of a diagram how they would find the acceleration of the trolley as it rolled down the slope. Your description should include all measurements needed and any calculations required.

8. Two women push a car and cause it to accelerate constantly from rest to 4m/s in 8s.

a) Calculate the acceleration of the car.

b) How long did it take for the car to reach a speed of 3 m/s?


SIC Physics Development Group MB

Acceleration 29. A cyclist is freewheeling down a hill accelerates constantly from 4 m/s

to 6.5 m/s in 6s.

a) What is the acceleration of the cyclist?

b) Assuming they maintain this acceleration, how fast will they be travelling 9s after the start

c) How long would it take the cyclist to reach a speed of 10.5 m/s after the start?

10. A ball bearing is placed at point A and rolls down a slope to point B.

Given that the acceleration is constant,

1)

2)

3)

4)

5)

6)

7)

8)

a)

a) Find the average speed between points A and B in ms-1

b) If the ball bearing takes 5s to travel from A to B what is the length of d in the diagram?

c) Calculate the acceleration of the ball bearing.



0.09 m/sd

A

Ball 10.9m

Ball 21.25m

Acceleration 2

11. A hot air balloon accelerates upwards from rest from the ground at 0.045m/s2. It maintains this acceleration for the first 40s of its flight. One Sandbag is then released which increases the acceleration of the balloon to 0.08m/s2.

a) What speed is the balloon 40 seconds after it has left the ground?

b) What is the speed of the balloon 20s after the sandbag has been released?

c) Draw a speed time graph for the flight of the balloon. (numerical values should be used)

d) Calculate the height of the balloon after 60s.

12. Two identical balls are dropped at the same time.

Ball 1 takes 0.5s to land. Ball B lands on the floor 0.15s after Ball A. Both balls accelerate towards the ground at 9.8m/s2.

What is the maximum speed of each ball?



time in s time in stime in s 10 20 30 40 50

2 4 6 8 10 12 5 10 15 20 25

Acceleration from Velocity-Time Graphs

1. Use the graphs below to calculate the acceleration over the interval shown.

(a) (b) (c)

(d) (e) (f)



velocity

velocityin m/s

velocityin m/s

25201510 5 0

10 8 6 4 2 0

5040302010 0

velocityin m/s

time in s

velocityin m/s

time in s

Velocity

In m/

time in s

25201510 5 0

10 8 6 4 2 0

5040302010 0

10 20 30 40 50

2 4 6 8 10 12 5 10 15 20 25

Helpful HintVelocity-time graphs can be used to calculate the acceleration (a) of an object.e.g. From the graph: initial speed (u) = 10 m/s

final speed (v) = 30 m/stime taken (t) = 8 s

So, using: a = v - u a = 30 - 10 = 25 m/s2 2 4 6 8 10 t 8

302010 0

velocityin m/s

time in seconds

Acceleration from Velocity-Time Graphs2. The graph below shows the journey of a car over a 20s interval.

Use the graph to calculate the acceleration of the car between:(a) 0 and 10 seconds (b) 10 and 20 seconds.

2 4 6 8 10 12 14 16 18 20 time in s3. Use the speed time graph below to calculate the acceleration of a

hovercraft between:(a)A and B(b)B and C.

45 90 time in s1.2.3.4. A car changes from 4th to 3rd to 2nd gear as it approaches traffic lights

set at red. The speed time graph representing the motion is shown below.Use the graph to calculate the deceleration of the car in each gear.

speedin m/s

5. Lorry drivers use tachographs to record information about their journeys.

A section of one journey is represented by the the graph below.



2 4 6 8 10 12 14 16 18 time in s

353025201510 5 0

velocity in m/s

25

Velocity in m/s

A0

B C

1816141210 8 6 4 2 0

25201510 5 0

Acceleration from Velocity-Time Graphsvelocity

in m/s

10 20 30 40 50 60 70 80 90 100 time in s

(a) During what time interval was the lorry’s acceleration greatest?(b) When did the lorry stop?(c) Calculate the deceleration of the lorry before if finally stopped.

6. Draw speed time graphs to represent the following motions:

(a) a motor cycle accelerating at 2m/s2 for 8 seconds from rest.(b) a Honda Civic accelerating at 5m/s2 for 10 seconds from rest.(c) a train accelerating at 2·5m/s 2 for 7 seconds from rest.



25201510 5 0

Acceleration 31. A Jaguar can reach 27 m/s from rest in 9.0 s. What is its acceleration?

2. The space shuttle reaches 1000 m/s, 45 s after launch. What is its acceleration?

3. A car reaches 30 m/s from a speed of 18 m/s in 6 s. What is its acceleration?

4. A train moving at 10 m/s increases its speed to 45 m/s in 10 s. What is itsacceleration?

5. A bullet travelling at 240 m/s hits a wall and stops in 0.2 s. What is its acceleration?

6. A car travelling at 20 m/s brakes and slows to a halt in 8 s. What is the deceleration?

7. Describe how you would measure the acceleration of a small vehicle as it runs down a slope in the laboratory.

8. On approaching the speed limit signs, a car slows from 30 m/s to 12 m/s in 5 s. What is its deceleration?

9. A bowling ball is accelerated from rest at 3 m/s2 for 1.2 s. What final speed will it reach?

10. How long will it take a car to increase its speed from 8 m/s to 20 m/s if it accelerates at 3 m/s2?

11. A cyclist can accelerate at 0.5 m/s2 when cycling at 4 m/s. How long will she take to reach 5.5 m/s ?



Acceleration 3

12. The maximum deceleration a car’s brakes can safely produce is 8 m/s2 What will be the minimum stopping time if the driver applies the brakes when travelling at 60 mph (27 m/s)

13. The table below gives some performance figures for cars.

Car Time for 0 – 60 mph (s)

Max. speed in mph

Mondeo 1.8 LX 10.2 122Peugeot 106 XN 1.1

12.5 103

Renault Clio RL 14.3 95Nissan Micra 1.0S 15.2 89Porsche Boxster 6.5 139

a) Which car has the smallest acceleration?b) Which car has the largest acceleration?c) Assuming that the acceleration remained constant, how long would it take for the following cars to reach their top speed?

i) Mondeo ii) Porsche



Miscellaneous Questions1. A woman is driving along a poorly lit section of the M8. Just as she passes

a sign indicating that the next exit is 400 m away she notices that a lorry has jack-knifed across the exit road.A speed time graph of her journey from the moment she passed the exit sign is shown below.

Speed 50in m/s 45

40 35 30 25 20

15 10

5 0

(a) When does the woman apply the brakes?.(b) Why does she not brake as soon as she sees the accident?(c) How far does she travel between seeing the accident and stopping?(d) Re-draw the speed time graph of the journey which would have been produced if the road had been wet.



5 10 15 20 25 30 35 40 time in s

Miscellaneous Questions2. Crash test dummies are placed in car seats mounted on

car simulation rigs and then projected towards crash barriers during seat belt trials. A speed time graph

of the trial is plotted

Use the graph to find out :(a) when the car strikes the barrier(b) the acceleration of the car before it strikes the crash barrier(c) the length of the test track.

3. An extract from a train time table is shown below:

Station Departure time

Distance (km)

Greenock 1015 0Paisley 1040 25

Hillington East 1046 32Glasgow Central 1055 40

(a) What was the average speed for the whole journey?(b) Between which two stations was the train going fastest?(c) A section of the train 50 metres long takes 4·2 seconds to enter a

tunnel . Calculate the instantaneous speed of the train at this entry point.(d) How could the value calculated in € be made more accurate?



SolutionsSpeed Distance Time Questions P 21. 9000m2. 300s3. 28.57 m/s4. 7.14 m/s5. 525m

6. 1.25 x 10-3m/s7. 2000s8. 12.5 m/s9. 3360m10. 285.71 s

Calculator Exercises P3.4Rounding offa. 0.11b. 0.33c. 0.49d. 556.49e. 26.31f. 23.61g. 105.66h. 31.19

EXP Practicea. 1.5 x 1013

b. 3.58 x 1036

c. 2.28 x 1051

d. 1.2 x 1019

e. 1.54 x 1018

f. 112.5g. 6.8 x 10-12

h. 1.38 x 10-6

i. 1.81 x 10-7

j. 1.12 x 10-10

k. 8.57 x 10-65

l. 833.33m. 19561.5n. 2.4 x 1021

Average Speed P 5, 6, 7, 8, 91)

1.1. (a)5 m/s

(b)5 m/s(c)12.5 m(d)880 m(e)0.05 s(f)200 s

2. 125 m/s3. 2 400 m4. 667 s5. 192 m/s6. 780 m7. 5714 s

8. 120 000 m9. 55556 s10. 20 625s (573

h)11. 1042 m/s12. 28571 m/s13. (a)2328 m/s

(b)Perth & Dundee14. (a) 3 m/s

1. 5 s15. (a) 70 km/h

(b)1 h 40 min(c)82.5 km/h

16. (a)480m

(b)13.71 s(c) After 15s cheetah is still 5m behind Antelope. Antelope escapes!

17. (a) Donald(b) Mickey’s 82.95 m/s(c) Mickey’s 78.35m/s

Donald 77.84 m/sGoofy 80.00 m/s

(d)Goofy – highest average speed

Instantaneous Speed P 10, 11, 121. (a) 02 m/s (b) 0.15 m/s (c) 7.32 x 10-3s (d) 0.175 m

(e) 0.4 m (f) 5.38 x 10-3 s2. 1.46 m/s

3. A – 8.00 m/s

B – 7.69 m/sC – 6.67 m/s


©GMV Science. Photocopiable only by the purchasing institution; Physics: Mechanics and Heat (Int2) – Student Material; SIC Development Group

SolutionsD – 6.90 m/sE – 8.00 m/sF – 8.33 m/s

a. Fb. C

4. 105.63 m/s

5. 4 m/s

Mixed Speed, Distance, Time Questions P 13. 141. 8 m/s2. Distance between two

points e.g. lamp-posts measured using a metre stickTime to travel between two points measured using a stopwatch,Speed = distance/time

3. 5.8 m/s4. a. 10 km/h

b. 2.8 m/s5. Distance between two

points e.g. lamp-posts measured using a metre stickTime to travel between two points measured using a stopwatch,Speed = distance/time

6. 17,000 m7. 2400 m8. 8000 s9. 3409 s = 57 minutes (56.8)

10. 2500 s = 42 minutes (41.7)

11. a. 24.3 m/sb. 28.3 m/sc. No stops between Glasgow and Falkirk. Between Glasgow and Edinburgh the train must stop twice at the station.

12. Use a light gate. When the vehicle passes through the light gate the time the beam is interrupted for is recorded on a timer. The length of the vehicle is measured using a metre stick. Speed = distance/time

13. 0.4 m/s14. .a. 0.75 m/s

b. 1.49 m/s

Speed-Time Graphs P 151. a. AB – constant speed

BC – negative accelerationb. AB – acceleration BC – constant speed

CD – accelerationc. AB – negative acceleration BC – zero speed CD – acceleration DE – negative acceleration

2. Graphs to be drawn



6 knots

SolutionsUsing Speed-Time Graphs to Calculate Distance P 16, 17, 18, 19

1. a. 20 mb. 180 mc. 650 md. 300 me. 550 mf. 300 mg. 693 mh. 4000 mi. 220 m

2. a. 8 s after seeing accidentb. 200 mc. 250 m

3. a. 0 – 50 s acceleration 50 – 70 s constant speed 70 – 80 s acceleration 80 – 90 s constant speedb. 1700 m

4. a. 0 – 20 s constant speed20 – 30 s negative acceleration

30 – 40 s constant speed40 – 50 s negative acceleration50 – 60 s constant speed60 – 70 s negative acceleration70 – 80 s constant speed80 – 90 s negative accelerationb. 1100 m

5. a. At 10 secondsb. 160m

6. a. 500 mb. deceleration for 560m so that the rocket reaches a point 20m above the Moon and hovers.

7. a. After 5sb. 125mc. 5.7 m/s

Vectors and Scalars 1 P 20, 21, 221. A vector quantity has

magnitude(size) and direction. A scalar quantity has magnitude only

2. VectorDisplacement, Velocity, Acceleration, Force, WeightScalarTime, Speed, Distance, Mass, Energy

3. 224 m at 117⁰4. a. 100 m

b. 71 m at 135⁰5. a. 13 km

b. 9.8 km at 024⁰

6. a. 70 mb. 7 m/sc. 50 m at 143⁰d. 5 m/s at 143⁰

7. a. 1400 mb. 1000 m at 037⁰c. 1.6 m/sd. 1.1 m/s at 037⁰

8. a. 13 kmb. 5.2 km/hc. 9.2 km at 319⁰d. 3.7 km/h at 319

9. a. 7 km/hb. 5 km/h at 053

10. a. 120 m



Solutionsb. 45m at 063⁰c. 2 m/sd. 0.75 m/s at 063⁰

11. a. 10 m/s at 037⁰b. 120m

12. 130.9 m/s at 353⁰

13. a.

b. 6.3 knots at 288⁰14. 34.6 m/s at 030⁰

Vectors and Scalars 2 P 23, 241. A vector quantity has

magnitude and direction. A scalar quantity has magnitude only.

2. Distance just has magnitude – e.g. 6m.Displacement has magnitude and direction e.g. 6 m due N.

3. a. 2 km Westb. 3.6 km

4. a. 1.5 m/sb. 0.83 m/s West

5. a. 400 mb. 0c 8.3 m/sd. 0



Solutions6. a. 800 m

b. 0c. 7 m/sd. 0

7. a 30 km North b. 50 kmc. 30 km/h North

d. 50 km/h8. a. 140 km

b. 100 km at 053c. 70 km/hd. 50 km/h at 053

Velocity-Time Graphs P 25, 261. a. acceleration for first 10 s

then constant velocityb. 1.5 m/s2

c. 75md, 525m

2. a. 30 – 90 sb. I 1 m/s2

ii -2 m/s2

c. 225 md.2475 me. 23.6m/s

3. Draw a graph4. a. 16 m/s

b. 288mc, 12 m/s

5. a. 0.3 m/s2

b. accelerating for 200m, constant velocity for 160 m

6.7.8.

Acceleration 1 P27,28.291. a. 2 m/s2

b. 4 m/s2

c. 9 m/sd. 240 m/se. 4 sf. 9 s

2. 0.5 m/s2

3. 0.875 m/s2

4. 10 m/s2

5. 0.25 m/s2

6. 1.25 m/s2

7. 1.5 m/s2

8. 0.5 m/s2

9. 0.75 m/s2

10. 0.4 m/s2

11. 0.2 m/s12. 9.5 s13. 30 s14. a. 2 m/s

b. 3.6 m/s15. 13.5 m/s16. 15.2 m/s



SolutionsAcceleration 2 P30,31,32

1. Acceleration is the change in velocity per second of an object.

2. The velocity changes by 4 m/s every second.

3. a. 12 m/sb. 18 m/sc. 30 m/sd.54 m/s

4. 2 m/s2

5. -22.5 m/s2

6. a. 9.8 m/s2

b. Use a light gate. Measure the diameter of the ball and the time taken to interrupt the light beam.

7. Measure the length of the trolley using the metre stick.Set up the light gates at two points on the slope. Release

the trolley on the slope. Use the stopwatch to find the time for the trolley to travel from one light gate to the other. Find the time the light gates are interrupted for and calculate the speed at each point. Acceleration is the change in velocity divided by time taken between light gates.

8. a. 0.5 m/s2

b. 6s9. a, 0.42 m/s2

b. 7.78 m/sc. 15.5 s

10. a. 0.045 m/sb. 0.225 mc. 0.018 m/s2



SolutionsAcceleration from Velocity-Time Graphs P33, 34, 35

1. a. 0.3 m/s2

b. 12.5 m/s2

c. 0.24 m/s2

d. 0.5 m/s2

e. 5 m/s2

f. 0.27 m/s2. a. 2.5 m/s2

b. 1 m/s2

3. a. 0.56 m/s2

b. 0 m/s2

4. Gear 4 – 2 m/s2

Gear 3 – 0.75 m/s2

Gear 2 – 2 m/s2

5. a. 50 – 70 mb. 50 s and 100 sc. 083 m/s2

6.

7. (a)50 - 70 s(b)50 s and 100 s (c) 083 m/s2

Acceleration 3 P 36, 371. 3 m/s2

2. 22.2 m/s2

3. 2 m/s2

4. 3.5 m/s2

5. -1200 m/s2

6. -2.5 m/s2

7. Measure the velocity at two points, measure the time taken between the two points. The acceleration is the change in velocity

divided by the time taken between the two points.

8. -3.6 m/s2

9. 3.6 m/s10. 4s11. 3s12. 3.4s13. a. Nissan Micra 1.0s

b. Porsche Boxsterc. i. 20.7s ii. 15.1 s



SolutionsMiscellaneous Questions P 38, 39

1. a. 5 s after 2. seeing lorry

b. Reaction timec. 525 m

3. a. At 12 sb. 2.5 m/s2

c. 180 m4. a. 60 km/h (16.67 m/s)

b. Paisley – Hillington Eastc. 11.9 m/s



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Mixed Speed, Distance, Time Questions - Lesmahagow … · Web viewA car, starting from rest, reaches a speed of 15 metres per second in a time of 30 seconds. Calculate the acceleration