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LESSON 1 LINEAR MOTION

Introduction Linear motion is the motion a straight line and

the movement in a direction where forwards is positive and backwards is negative. Kinematics is the section of physics which studies the motions of objects without considering the effects that produce the motion. The study generally involves the analysis of the position of an object in relation to time. Dynamics is the section of physics which studies the causes of motion of an object. Distance ,d and Displacement, s Distance ,d is how far a body travels during a motion without considering any particular direction or the length of the path of an object. Distance is a scalar quantity and the value always positive. The unit of distance is metre (m) Displacement, s is distance traveled in a particular direction. Displacement, s = final position – initial position Displacement is a vector quantity and the value can be positive and negative depend on their directions. The unit of displacement is metre (m)

Diagram below shows the difference between distance and displacement.

Distance = Length of the road Displacement = Length of the line AB

If the motion in a straight line and in one direction , the magnitude of distance is same as the magnitude of displacement .

Speed and Velocity ,v Speed is the rate of change of distance. Speed = distance travelled time taken Average speed = total distance traveled total time taken

Speed is a scalar quantity and the value always positive. The unit of speed is metre per second (m s-1)

Velocity is the rate of change of displacement. Velocity = displacement time taken v = s t Average velocity = total displacement total time taken

Velocity is a vector quantity and the value can be positive and negative depend on their directions. The unit of velocity is metre per second (m s-1)

If an object moves in a circle with constant speed , it has different velocities at different points along the circle because the direction and hence the velocity of the object is always changing as shown in the following diagram.

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Acceleration, a and Deceleration (Retardation) Acceleration is the rate of change of velocity. Acceleration = change in velocity time taken Acceleration = final velocity – initial velocity time taken a = v - u t Negative acceleration is called as deceleration (retardation) Acceleration is a vector quantity The unit of acceleration or deceleration is metre per second per second (ms-2)

Extra notes 1 uniform = constant = same 2 increasing velocity = acceleration

3 decreasing velocity (slow down) = deceleration

4 zero velocity = the object is stationary (at rest)

5 negative velocity = the object moves in opposite direction

6 uniform velocity = zero acceleration 7 negative acceleration = deceleration

(retardation)

Example 1

A boy walks finish the following path PQ.

Find (a) total distance traveled (b) displacement

Solution

Example 2

Figure above shows runner runs 500 m towards east in 2 minutes and 1200m towards north in 4 minutes. Calculate his (a) average speed (b) average velocity Solution Example 3

An object accelerates uniformly along a straight line from a velocity of 10 m s-1 until 25 m s-1 in 5 s. Calculate (a) the acceleration of the object (b) the velocity of the object during the first 10

s of motion (c) the time taken to reach a final velocity 50

ms-1

Solution

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Using a ticker timer to analysing the motion

A ticker timer is connected to an alternating electricity supply (a.c.) and uses the mains electricity frequency of 50 Hz to make 50 ticks or vibrations every second. 1 tick is the time interval between one dot and the next dot on the tape. 50 ticks = 1 s 1 tick = 0.02s

Example 4

Based on the ticker tape above calculate (a) time taken (b) average velocity

Solution

Example 5

Based on the figure above, calculate the acceleration .

Solution

Example 6

The figure above shows a ticker tape contains 5 ticks for every interval AB.BC.CD and DE .Calculate the acceleration.

Solution

Example 7

The following figure shows a tape chart.

Calculate (a) the acceleration (b) the average velocity

Solution

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The type of motion based on ticker tape or tape chart (a)

The type of motion is

velocity acceleration

(b)

The type of motion is

velocity acceleration

(c)

The type of motion is

velocity acceleration

(d)

The type of motion is

velocity acceleration

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(e)

The type of motion is

velocity acceleration

Using a stroboscopic photograph to analysing the motion

Stroboscopic photograph is the taking of very short –exposure pictures of moving objects using a camera and a stroboscope. A stroboscope is a device for making a moving body intermittently visible in order to make appear stationary. The moving object appear ‘freeze’ when the stroboscope frequency at the same frequency of moving object. There are two types of stroboscopes: (i) Mechanical stroboscope

Stroboscopic photograph = number of slits x frequency stroboscope

frequency

or f = np

(ii) Electronic stroboscope ( multiflash stroboscope )

Stroboscopic photograph frequency = light flashes frequency

Example 8

The following figure a stroboscopic photograph shows a metal ball moves along a horizontal plane. The photograph is taken by using a camera and a mechanical stroboscope has 8 slits and rotates with frequency 5 Hz.

(a) State the type of motion of the metal ball. (b) What is the stroboscopic photograph

frequency (c) What is the time intervals between one

image and the next. (d) Calculate the average velocity of the metal

ball (e) What is the number of images in 30

seconds.

Solution

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Example 9 The following figure a stroboscopic photograph shows a trolley down an inclined plane. The photograph is taken by using a camera and an electronic stroboscope produces 20 flashes per second.

(a) State the type of motion of the trolley. (b) What is the stroboscopic photograph

frequency (c) What is the time intervals between one

image and the next. (d) Calculate

(i) the initial velocity (ii) the final velocity (iii) the acceleration

Solution

Using Equations of Linear Motion with Uniform Acceleration

The various equations of linear motions of an object with uniform acceleration are given as follows:

v = u + at ……………………….(1) s = u + v t ………………………..(2) 2

2

2

1atuts ………………………..(3)

v2 = u2 + 2as ………………………..(4)

Where s :…………………………………

u :………………………………...

v :………………………………...

a :…………………………………

t :…………………………………

Extra notes:

moves from rest : ………………………

finally it stops/brakes:…………………..

released from a height / fall freely from rest :……………………………………….

thrown vertically upwards:……………..

at maximum height :…………………….

Example 10

A car accelerates from rest to 25 m s-1 in 4 s. Find the acceleration of the car.

Solution

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Example 11

A bus accelerates uniformly along a straight line from a velocity 20 ms-1 until 30 ms-1 in 5 s. Calculate, (a) the acceleration (b) the total displacement travelled by the bus

Solution

Example 12 A construction worker accidentally knocks a brick from a building so that it falls in 4 s to the ground. Calculate (a) the velocity of the brick as it hits the ground (b) the distance fallen of the brick Solution

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TUTORIAL 1 1 A car moves with a constant velocity. The

acceleration of the car is A increased B decreased C zero D uniformly 2 Deceleration means the velocity of an object is A negative B positive C increased D decreased 3 The following diagram shows an object moves

with a constant speed 5 m s-1 in a circle.

The object is also moves with

A an acceleration B zero acceleration C constant velocity 4 The diagram shows a path of a moving object.

If AB = 5m , BC = 5m and CD = 7m ,find the total displacement of the object if it moves from A to D.

A 3m B 7m C 13 m D 17 m E 20 m

5 Ali rides a motorcycle with a constant speed 30

km h-1 . Bakar runs at a distance 100 m in 15 s. Chan rides a bicycle at distance 240 km in 10 hours.

Which comparison is true? A Speed of Ali = speed of Bakar B Speed of Ali = speed of Bakar = speed of

Chan C Speed of Ali > speed of Bakar

D Speed of Ali =speed of Chan > speed of Bakar E Speed of Bakar = Speed of Chan < speed of Ali

6 A tick on the ticker tapes is A the speed of the ticker timer B the frequency of the ticker timer C the distance between two consecutive dots D the time interval between two consecutive

dots 7 The frequency of a ticker timer is 50 Hz. The

time interval between 16 consecutive dots is

A 0.60 s B 0.44 s C 0.32 s D 0.30 s E 0.20 s

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8 Figure shows the ticker tape for the motion of a

trolley.

Which of the following statement is true?

A The velocity between in region DE is same as the velocity in region A B

B Frequency in region BC is greater than frequency in region DE

C The time in region AB is same as the time in region DE

D The velocity between in region CD is low 9 Based on the figure above , calculate the

average velocity.

A 0.2 ms-1 B 0.3 ms-1 C 0.4 ms-1 D 0.5 ms-1 E 0.5 ms-1

10 The diagram shows a ticker tape.

What is the average velocity between PQ

A 85 cms-1 B 170 cms-1 C 200 cms-1 D 240 cms-1 E 500 cms-1

11 The diagram shows a ticker tape.

What is the final velocity ? A 40 cms-1 B 120 cms-1 C 150 cms-1 D 267 cms-1 E 420 cms-1

12 The diagram shows a ticker tape to show the

motions of a trolley.

What is the acceleration of the trolley? A 2 ms-2 B 4 ms-2 C 5 ms-2 D 8 ms-2 E 10 ms-2

13 The diagram shows a ticker tape to show the

motions of a trolley.

What is the acceleration of the trolley?

A -5 ms-2 B - 50 ms-2 C - 500 ms-2 D 50 ms-2 E 500 ms-2

14 The following figure shows a tape chart.

Based on figure , which of the following is true?

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At the beginning of At the end of

motion motion A the velocity the acceleration unchanged increases B the velocity the acceleration

increases increases C the velocity the acceleration increases unchanged D the velocity the acceleration

unchanged unchanged 15 Which of the following shows an object moving

with decreasing acceleration ?

16 The diagram shows a stroboscopic photograph

of a ball moves on a smooth table.

Which of the following is true?

A The acceleration is constant B The velocity is increasing C The acceleration is zero D The velocity is zero

17 A stroboscope has 4 slits and rotates with

frequency 5 Hz. The time intervals between two successive images is

A 40.0 s B 2.0 s C 1.0 s D 0.4 s E 0.05 s

18 The diagram shows a stroboscopic photograph

shows an ice cube moves along a horizontal plane. The photograph is taken by using a camera and a mechanical stroboscope has 2 slits and rotates with frequency 25 Hz.

What is the velocity of the ice cube?

A 5 cms-1 B 25 cms-1 C 100 cms-1 D 250 cms-1

E 500 cms-1 19 The diagram shows a stroboscopic photograph

shows a ball moves along a horizontal plane. The photograph is taken by using a camera and an electronic stroboscope produces 50 flashes per second.

What is the average velocity of the ball. A 0. 5 ms-1 B 1.0 ms-1 C 1.5 ms-1 D 2.0 ms-1 E 3.0 ms-1

20 The diagram shows a stroboscopic photograph shows a boy down an inclined plane. The photograph is taken by using a camera and an electronic stroboscope produces 4 flashes per second.

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The acceleration of the boy is A 6 ms-2 B 12 ms-2 C 24 ms-2 D 32 ms-2 E 48 ms-2

21 A cyclist riding at a velocity 8 ms-1 and is

accelerating with 4 ms-2 . What is the velocity

of the cyclist after 5 s .

A 16 ms-1 B 20ms-1

C 24 ms-1 D 28 ms-1

E 32 ms-1

22 A rocket starts at velocity 2500 ms-1 and accelerates uniformly upwards at 20 ms-2 .

What is the velocity of the rocket after 4 minutes.

A 4800 ms-1 B 5000 ms-1

C 6800 ms-1 D 7300 ms-1

E 7500 ms-1

23 A trolley starts from rest and is uniformly

accelerated to speed of 12 cms-1 in 5 . What is

the distance travelled by the trolley?

A 16 cm B 24 cm C 28 cm D 30 cm E 42 cm

24 A car starts from rest and accelerates uniformly

and after travels at distance 45m the velocity

of the car is 20 ms-1 . What is the time taken?

A 4.5 s B 9.0 s C 13.5 s D 18.0 s E 22.4 s

25 A aero plane accelerates at 40 ms-2 in 10 s

to take off. What is the minimum length of the runway on the airfield ?

A 1000 m B 2000 m C 3000 m D 4000 m

E 5000 m 26 A car starts from rest and accelerates uniformly

. If the distance reached is 900 m after travels in 30 s, calculate the acceleration of the car.

A 5 ms -2 B 4 ms-2 C 3 ms-2 D 2 ms-2 E 1 ms-2

27 A lorry start from rest and accelerates at 10

ms-2. What is the velocity of the lorry after travels for a distance 20m ?

A 10 ms-1 B 20ms-1

C 40 ms-1 D 80 ms-1

E 100 ms-1

28 A car travels with a velocity 15 ms-1 . It then

accelerates uniformly and travels a distance of

12.5 m. If the velocity reached is 10 ms-1 find the

acceleration of the car.

A –5.0 ms-2 B –2.5 ms-2

C 2.5 ms-2 D 5.0 ms-2

E 7.5 ms-2

29 A car moves with a velocity 40 ms-1 . After the

brakes of the car is applied ,it moves 100 m more before coming to rest. Calculate the deceleration of the car.

A 4 ms-2 B 8 ms-2

C 12 ms-2 D 16 ms-2

E 20 ms-2

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30 A lorry moves with a velocity 20 ms-1. After the

brakes of the car is applied it moves for a distance 4 m before coming to rest. What is the time taken before it stops?

A 1.0 s B 0.8 s C 0.6 s D 0.4 s E 0.2 s

31 A stone fall freely from rest through a height of 5

m. What is the velocity of the stone when it hits the ground.

A 5 ms-1 B 10 ms-1

C 15 ms-1 D 20ms-1

E 30 ms-1

32 A coconut falls vertically to the ground. If the

coconut takes 1.5 s to fall to the ground, calculate the height from which it fell. A 8.45 m B 11.25 m C 15.00 m D 22.50 m

E 31.25m 33 A metal sphere falls 125m vertically to the

ground. What is the time the metal sphere takes to reach the ground?

A 2 s B 4s C 5 s D 8s E 10 s

34 A ball is thrown vertically upwards from the

ground with a velocity of 20 ms-1. Calculate the

maximum height reached.

A 60 m B 40 m C 30 m D 20 m E 10 m

35 The table (a) and (b) shows the distances travelled and the times taken for four students in a competition

Student Distance/m Time/ s

P 100 20

Q 120 20

Table (a)

Student Distance/ m Time/ s

R 100 20

S 100 15

Table (b) (a) Compare the speeds of the

(i) student P and student Q

………………………………………… (ii) student R and student S

…………………………………………

(b) State the relationship between (i) the speed and the distance in table

(a) ……………………………………………

………………………….........................

(ii) the speed and the distance in table (b)

……………………………………………

……………………….............................

(c) Based on the relationship in (b),state the definition of speed.

…………………………………………………

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36 Figure (a) shows a ticker tape for the motion of a trolley . Figure (b) shows a stroboscopic photograph for the motion of a glider .

(a) Observe the figure (a) and (b) and state

two similarities between the positions of the ticks on the ticker tape and the images on the stroboscopic photograph. .................................................................... …………………………………………………

(b) Relate the similarities in (a) to explain a concept of motion.

…………………………………………………

…………………………………………………

(a) What will happen to the ticker timer if it is connected to a d.c. supply ?

…………………………………………………

(d) What will happen to the motion of the glider if the slope of the declined plane is increased?

…………………………………………………

37 The diagram shows a tape chart . The chart is produced by the motion of a trolley.The ticker timer used a supply voltage 12 V a.c. at 50 Hz.

(a) Describe the type of motion is shown in the

tape chart.

....................................................................

.................................................................... (b) What is the time interval between two

consecutive dots ?

.................................................................... (c) Calculate

(i) the minimum velocity

(ii) the maximum velocity

(iii) the average velocity.

(iv) the acceleration.

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38 The following equation shows the equations of

linear motion of an object with uniform acceleration.

v = u + at (a) (i) What is meant by the symbol of ‘a’

………………………………………….. (ii) Give the definition of the symbol of ‘a’ ............................................................ (b) (i) What is the information can you get

from the term of ‘at’ …………………………………….......

(ii) What is the S.I. units for the term of ‘at’

………………………………………….. (c) The above equation can also be used for

an object in state of free-fall. A stone fall freely to the ground from rest in 4 s. (i) What is meant by ‘fall freely’?

…………………………………………………

(ii) Calculate the velocity of the stone when it hits the ground.

39 Each diagram below show two positions of a

student on a swing. The initial position in each figure is different.

Observe the positions of each of the swing in each diagram and the appearance of the student when she swings.

Based on the observations:

(a) State one suitable inference that can be made.

(b) State one appropriate hypothesis for an investigation.

(c) With the use of apparatus such as trolley, ticker timer and other apparatus , describe an experimental framework to test your hypothesis. In your description , state clearly the following:

(i) Aim of the experiment (ii) Variables in the experiment

(iii) List of apparatus and materials (iv) Arrangement of the apparatus (v) The procedure of the experiment

which include the method of controlling the manipulated variable and the method of measuring the responding variable.

(vi) Way you would tabulate the data (vii) Way you would analysis the data