UNIT 1 MOTION. What do you think? If you walk from home to school, and then immediately return to your home. If the distance from your home to school

UNIT 1UNIT 1

MOTIONMOTION

What do you think?What do you think?If you walk from home to school, and If you walk from home to school, and then immediately return to your then immediately return to your home. If the distance from your home. If the distance from your home to school is 15 m, what is home to school is 15 m, what is your ….your ….

– Distance?Distance?

– Displacement?Displacement?

– What are some of the units we can What are some of the units we can measure displacement with?measure displacement with?

– What are some of the tools we use to What are some of the tools we use to measure displacement?measure displacement?

Distance or DisplacementDistance or DisplacementDistance – Distance – the amount of space between two objects or points

Displacement – Displacement – the overall change the overall change in position of an object.in position of an object.

Calculating DisplacementCalculating DisplacementTo calculate the displacement of an To calculate the displacement of an object you must know the beginning object you must know the beginning and ending point.and ending point.

d = xd = xff - x - xii

d = displacementd = displacementXXf f = final position= final positionXXii = initial position = initial position

Sample Problem 1Sample Problem 1 Brendan walked from Walmart to his Brendan walked from Walmart to his home, and there existed 300 m home, and there existed 300 m between the two. What is the…between the two. What is the…



Sample Problem 2Sample Problem 2Miranda walked from School to Miranda walked from School to Subway and back at noon. If 20m Subway and back at noon. If 20m existed between the school and existed between the school and Subway, what is the ….Subway, what is the ….



Speed or Velocity?Speed or Velocity?SpeedSpeed – is a measurement that describes – is a measurement that describes how far an object has moved in a certain how far an object has moved in a certain period of time without indicating direction.period of time without indicating direction.

VelocityVelocity – is a measurement that – is a measurement that describes how far an object has moved in describes how far an object has moved in a certain period of time, while at the same a certain period of time, while at the same time indicating directiontime indicating direction

Velocity calculations use displacementVelocity calculations use displacement

Speed calculations use distanceSpeed calculations use distance

Both velocity and speed calculations Both velocity and speed calculations use time.use time.

– TimeTime – the duration between two events – the duration between two events and is usually measured in seconds, and is usually measured in seconds, minutes, or hoursminutes, or hours

Relating Velocity to Displacement Relating Velocity to Displacement and Timeand Time

Average Velocity (vAverage Velocity (vaveave)) - is the - is the overall displacement divided by the overall displacement divided by the total time it took to traveltotal time it took to travel

The equation for average velocity is:The equation for average velocity is:

tdvave

Instantaneous velocity Instantaneous velocity – the velocity at – the velocity at which an object is traveling at a particular which an object is traveling at a particular instant. instant.

– It is not affected by its previous velocity, or by It is not affected by its previous velocity, or by how long the object has been moving.how long the object has been moving.

– The speedometer and radar gun were designed The speedometer and radar gun were designed to measure instantaneous velocity.to measure instantaneous velocity.

Constant Velocity (uniform Constant Velocity (uniform motion)motion) – occurs when the velocity – occurs when the velocity of an object remains the same over of an object remains the same over an extended period of timean extended period of time

– E.g. Using Cruise Control on your carE.g. Using Cruise Control on your car

Sample Problem 1Sample Problem 1Keri bikes to school, a total Keri bikes to school, a total displacement of 450.0 m (SW). She displacement of 450.0 m (SW). She has to slow down twice to cross busy has to slow down twice to cross busy streets, but overall the journey takes streets, but overall the journey takes her 1080 seconds. What is Keri’s her 1080 seconds. What is Keri’s average velocity during the trip?average velocity during the trip?

ANSWER 1ANSWER 1

∆∆d = 450.0 md = 450.0 m∆∆t = 1080 st = 1080 sVVaveave = ? = ?

= 450 m/1080 s= 450 m/1080 sVVavav = 0.417 m/s = 0.417 m/s

tdvav

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Sample Problem 2Sample Problem 2Laura is trying to predict the time Laura is trying to predict the time required to ride her bike to the required to ride her bike to the nearby beach. She knows the nearby beach. She knows the distance is 5000 m and, from other distance is 5000 m and, from other trips, that she can average about trips, that she can average about 5 m/s (E) including slowing down for 5 m/s (E) including slowing down for climbing hills. Predict how long the climbing hills. Predict how long the trip will take.trip will take.

Answer 2Answer 2

∆∆t = 1 000 st = 1 000 s

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Sample Problem 3Sample Problem 3Derek has a summer job helping with Derek has a summer job helping with bison research. He notes that they bison research. He notes that they graze (move and eat grass) at an graze (move and eat grass) at an average velocity of about 0.03 m/s average velocity of about 0.03 m/s (NW) for about 25200 s/d. What is (NW) for about 25200 s/d. What is the displacement, in meters, will the the displacement, in meters, will the herd travel in two weeks (14 d)?herd travel in two weeks (14 d)?

Answer 3Answer 3

∆∆d =d =

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HomeworkHomeworkAaron is riding a cow at a velocity of Aaron is riding a cow at a velocity of 0.005 m/s for a period of 15552000s. 0.005 m/s for a period of 15552000s. How far did Aaron travel? How far did Aaron travel?

Sally is driving for 18000 s if she Sally is driving for 18000 s if she drove 5000 m what was her velocity?drove 5000 m what was her velocity?

HomeworkHomeworkQuestions 1 – 6 on page 358Questions 1 – 6 on page 358

Changing UnitsChanging UnitsAll final calculations in Physics should be in All final calculations in Physics should be in meters and secondsmeters and seconds

UnitUnit Equivalence Equivalence to 1 mto 1 m

KmKm 1000 m1000 mhmhm 100 m100 mdd 10 m10 mmm 1 m1 mdmdm 0.1 m0.1 mcmcm 0.01 m0.01 mmmmm 0.001 m0.001 m

UnitUnit Equivalence Equivalence to 1 sto 1 s

1 day1 day 86 400 s86 400 s1 h1 h 3 600 s3 600 s1 min1 min 60 s60 s

Convert the following to the Convert the following to the appropriate units:appropriate units:

1) 2 hours1) 2 hours2) 100 km2) 100 km3) 7 cm3) 7 cm4) 5 min4) 5 min5) 2 km/s5) 2 km/s6) 10 m/h6) 10 m/h7) 500 km/h7) 500 km/h

What do you do when you have two What do you do when you have two different velocities?different velocities?

In some problems you will be given more In some problems you will be given more than one velocity (an initial velocity and a than one velocity (an initial velocity and a final velocity)final velocity)

In most cases your initial velocity is 0 and In most cases your initial velocity is 0 and is not stated in the problemis not stated in the problem

In other cases the initial velocity is given a In other cases the initial velocity is given a concrete value due to the fact that the concrete value due to the fact that the object is in motion at the beginning of the object is in motion at the beginning of the problem and the velocity is altered at some problem and the velocity is altered at some point (either faster or slower).point (either faster or slower).

Two VelocitiesTwo Velocities

In situations where there are two velocities In situations where there are two velocities (and only displacement and time) in most (and only displacement and time) in most cases we will use the following formulacases we will use the following formula

d = d = (v(vff + v + vii)) t t 22d = displacementd = displacementvvff = final velocity = final velocityvvii = initial velocity = initial velocityt = timet = time

Sample Problem 1Sample Problem 1Kristen is sitting at a red light in her Kristen is sitting at a red light in her red corvette. The light turns green red corvette. The light turns green and Kristen instantaneously guns the and Kristen instantaneously guns the engine of her car. If 10 seconds later engine of her car. If 10 seconds later Kristen is traveling at a velocity of 90 Kristen is traveling at a velocity of 90 km/h in a northern direction (in a 50 km/h in a northern direction (in a 50 km/h speed zone) what is her km/h speed zone) what is her displacement?displacement?

AnswerAnswerd = d = (25 m/s + 0 m/s)(25 m/s + 0 m/s) 10s 10s

22d = 125 md = 125 m

Sample Problem 2Sample Problem 2Brendan and Amber are at Walmart Brendan and Amber are at Walmart looking for a video game. They are walking looking for a video game. They are walking down the video game isle at a velocity of down the video game isle at a velocity of 0.5 m/s. They happen to spot Miss Cook at 0.5 m/s. They happen to spot Miss Cook at the store and they want to avoid her the store and they want to avoid her seeing them in the isle with the video seeing them in the isle with the video games, so they quickly leave the isle games, so they quickly leave the isle traveling at a velocity of 0.9 m/s. If it only traveling at a velocity of 0.9 m/s. If it only took Brendan and Amber 3 seconds to exit took Brendan and Amber 3 seconds to exit the isle, what was their displacement?the isle, what was their displacement?

Sample Problem 3Sample Problem 3Mike and Brandon are driving in Mike and Brandon are driving in Sussex at 60 km/h towards Sussex at 60 km/h towards Apohauqui. Brandon spots a Apohauqui. Brandon spots a hugehuge pothole in the road and slows down pothole in the road and slows down to a velocity of 20 km/h to drive to a velocity of 20 km/h to drive through the pothole. If 30 seconds through the pothole. If 30 seconds later the boys have driven over the later the boys have driven over the pothole, what was their displacement pothole, what was their displacement from the time that Brandon first from the time that Brandon first noticed the pothole?noticed the pothole?

Sample Problem 4Sample Problem 4Jalise is walking towards the mall at a Jalise is walking towards the mall at a velocity of 0.4 m/s. She sees a 50% velocity of 0.4 m/s. She sees a 50% off sale sign in the window and starts off sale sign in the window and starts running towards the store. If her running towards the store. If her final velocity is 1.3 m/s (she is final velocity is 1.3 m/s (she is wearing stilettos). If the wearing stilettos). If the displacement between the store and displacement between the store and where she spotted the sign is 0.6 km, where she spotted the sign is 0.6 km, how long did it take her to reach the how long did it take her to reach the store. store.

Sample Problem 5Sample Problem 5Colin and Corey are snowboarding at Colin and Corey are snowboarding at Poley Mountain. If at the top of the Poley Mountain. If at the top of the hill they are traveling at a velocity of hill they are traveling at a velocity of 3 m/s and it takes them a total time 3 m/s and it takes them a total time of 2 minutes to reach the bottom of of 2 minutes to reach the bottom of the hill, a displacement of 500 m. the hill, a displacement of 500 m. How fast were Colin and Corey How fast were Colin and Corey traveling at the bottom of the hill?traveling at the bottom of the hill?

Sample Problem 6Sample Problem 6Sam is snowshoeing around the trail Sam is snowshoeing around the trail behind the school for gym class. behind the school for gym class. Sam has never used snowshoes Sam has never used snowshoes before but quickly picks up the before but quickly picks up the technique. If Sam is traveling at a technique. If Sam is traveling at a velocity of 0.6 m/s at the end of the velocity of 0.6 m/s at the end of the trail and it took her a 20 minutes to trail and it took her a 20 minutes to travel the 1 km long route. What was travel the 1 km long route. What was Sam’s initial velocity?Sam’s initial velocity?

HomeworkHomeworkJackson is driving towards the train station Jackson is driving towards the train station with a velocity of 30 m/s. If it takes with a velocity of 30 m/s. If it takes Jackson 10 minutes to reach and stop at Jackson 10 minutes to reach and stop at the train station how far did he travel.the train station how far did he travel.

Sally is riding her bike to the local KFC. It Sally is riding her bike to the local KFC. It takes Sally 10 min to reach KFC which is takes Sally 10 min to reach KFC which is 4.7 km away. What is Sally’s initial 4.7 km away. What is Sally’s initial velocity if she ends the trip with a velocity velocity if she ends the trip with a velocity of 17 m/s. of 17 m/s.

Review of Variables in GraphingReview of Variables in GraphingIndependent VariableIndependent Variable – the – the variable that changes over the variable that changes over the course of an experiment in order to course of an experiment in order to compare results.compare results.

Dependent VariableDependent Variable – the variable – the variable that changes as a result to changes that changes as a result to changes in your independent variablein your independent variable

Graphing ExpectationsGraphing ExpectationsThe title of your graph must be The title of your graph must be placed at the top of your graphplaced at the top of your graphLabel your x and y axis with the Label your x and y axis with the appropriate terms and unitsappropriate terms and unitsLabel the end of your axis with either Label the end of your axis with either an x or yan x or yPick an appropriate scale for your Pick an appropriate scale for your valuesvalues

Displacement Time GraphsDisplacement Time GraphsWhen observing or constructing a When observing or constructing a displacement time graph your time is displacement time graph your time is always your independent variable (x-axis), always your independent variable (x-axis), while your displacement is your dependent while your displacement is your dependent variable (y-axis)variable (y-axis)

The slope represents the velocity (the The slope represents the velocity (the relationship between the dependent and relationship between the dependent and independent variable)independent variable)

– The greater the velocity the larger the slopeThe greater the velocity the larger the slope

How to Interpret Displacement How to Interpret Displacement Time GraphsTime Graphs

Time (s)x

y

Disp

lace

men

t (m

) In this graph the object is not in motion.

How can you tell this from the graph?


Time (s)x

y

Disp

lace

men

t (m

) In this graph the object is moving with a constant velocity.


In this graph the velocity is not constant.


How would you calculate average velocity for this graph?

Time (s)x

y

Disp

lace

men

t (m

)


Time (s)x

y

Disp

lace

men

t (m

)

In this graph there is no velocity.



Time (s)x

y

Disp

lace

men

t (m

)

In this graph you would solely use the values of xi and xf to determine the displacement of the object, in order to calculate velocity. Why?

How to construct a displacement How to construct a displacement time graphtime graph

Plot your points using an appropriate Plot your points using an appropriate scale along your x and y axisscale along your x and y axis

Chose two points from your line of Chose two points from your line of best fit and use them to calculate the best fit and use them to calculate the slope of the line (velocity)slope of the line (velocity)

Graphing displacement and timeGraphing displacement and timed d

(m)(m)t t

(s)(s)11 2244 5588 8899 111199 1515

012345678910

2 5 8 11 15

Defining AccelerationDefining AccelerationAcceleration (a)Acceleration (a) – is the rate of change in – is the rate of change in velocity and is calculated by the ratio of the velocity and is calculated by the ratio of the change in velocity (∆v) to the time interval (∆t) change in velocity (∆v) to the time interval (∆t) during which this change occurred. during which this change occurred.

Constant AccelerationConstant Acceleration – the same change in – the same change in speed (∆v) occurs in each equal interval of time speed (∆v) occurs in each equal interval of time (∆t)(∆t)

Average Acceleration (aAverage Acceleration (aavav)) – is the average – is the average rate of change in velocity of an object.rate of change in velocity of an object.

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Sample Problem 1Sample Problem 1Dustin accelerates at an average Dustin accelerates at an average rate of 2.5 m/srate of 2.5 m/s2 2 for 1.5 s. What is his for 1.5 s. What is his change in velocity at the end of 1.5s?change in velocity at the end of 1.5s?

ANSWER 1ANSWER 1

∆∆v = a∆tv = a∆t∆∆v = (2.5 m/sv = (2.5 m/s22)(1.5s))(1.5s)∆∆v = 3.8 m/sv = 3.8 m/s

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Sample Problem 2Sample Problem 2Ryan M. is skateboarding down a hill Ryan M. is skateboarding down a hill and changes his velocity from rest to and changes his velocity from rest to 1.9m/s. If the average acceleration 1.9m/s. If the average acceleration down the hill is 0.40m/sdown the hill is 0.40m/s22, for how , for how long was Ryan on the hill?long was Ryan on the hill?

ANSWER 2ANSWER 2∆∆t = ?t = ?a = 0.40 m/sa = 0.40 m/s22

∆∆v = 1.9 m/sv = 1.9 m/s

∆∆t =4.8 st =4.8 s

HomeworkHomework1.1. Shannon is driving through Tim Horton’s drive Shannon is driving through Tim Horton’s drive

thru with an acceleration rate of 6 m/sthru with an acceleration rate of 6 m/s22 for 60 s. for 60 s. What was her velocity?What was her velocity?

2.2. Josh and Sam are best friends who are skiing at Josh and Sam are best friends who are skiing at Poley. If they start at the top of the hill with a Poley. If they start at the top of the hill with a velocity of 0 m/s and at the bottom they have a velocity of 0 m/s and at the bottom they have a velocity of 10 m/s. If it takes them 50 s to get to velocity of 10 m/s. If it takes them 50 s to get to the bottom of the hill what is their rate of the bottom of the hill what is their rate of acceleration?acceleration?

3.3. Maddy is horse back riding down Main Street. Maddy is horse back riding down Main Street. Maddy wants to make the green light so she Maddy wants to make the green light so she accelerates her horse at a rate of 0.5 m/saccelerates her horse at a rate of 0.5 m/s22 to a to a velocity of 6 m/s. How long did this take Maddy?velocity of 6 m/s. How long did this take Maddy?

Kimbo Slice is riding a tricycle from Kimbo Slice is riding a tricycle from end of the octagon to the other. If it end of the octagon to the other. If it takes Kimbo Slice 500 s to cover the takes Kimbo Slice 500 s to cover the 12 m. What was Kimbo Slice’s 12 m. What was Kimbo Slice’s acceleration?acceleration?

Refining the Acceleration EquationRefining the Acceleration EquationBoth the initial velocity vBoth the initial velocity v ii and the and the final velocity vfinal velocity vff affect your affect your acceleration.acceleration.

∆∆v = vv = vf f – v– vii

The acceleration equation can now The acceleration equation can now be written as:be written as:

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Sample Problem 3Sample Problem 3Kerrin is moving at 1.8m/s near the Kerrin is moving at 1.8m/s near the top of a hill. 4.2 s later she is top of a hill. 4.2 s later she is traveling at 8.3 m/s. What is her traveling at 8.3 m/s. What is her average acceleration?average acceleration?

ANSWER 3ANSWER 3VVii = 1.8 m/s = 1.8 m/s∆∆t = 4.2st = 4.2sVVf f = 8.3 m/s= 8.3 m/sa = ?a = ?

a = 1.5 m/sa = 1.5 m/s22

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12

Sample Problem 4Sample Problem 4A bus with an initial velocity of 12m/s A bus with an initial velocity of 12m/s accelerates at 0.62 m/saccelerates at 0.62 m/s22 for 15 s. for 15 s. What is the final velocity of the bus?What is the final velocity of the bus?

VVii = 12 m/s = 12 m/sa = 0.62 m/sa = 0.62 m/s22

∆∆t = 15 st = 15 sVVf f = ?= ?

VVff = 21 m/s = 21 m/s

Acceleration While Slowing DownAcceleration While Slowing Down Acceleration while slowing down is Acceleration while slowing down is calculated in the same manner as calculated in the same manner as acceleration while speeding up. The acceleration while speeding up. The only difference is that the only difference is that the acceleration is represented with a acceleration is represented with a negative sign.negative sign.

Sample Problem 5Sample Problem 5In a race, a car traveling at 100km/h In a race, a car traveling at 100km/h comes to a stop in 5.0 s. What is the comes to a stop in 5.0 s. What is the average acceleration?average acceleration?

VVii = 100 km/h = 100 km/hVVff = 0 = 0∆∆t = 5.0 s t = 5.0 s a = ?a = ?

HomeworkHomeworkNick is walking down the street Nick is walking down the street drinking pop with a velocity of 3 m/s. drinking pop with a velocity of 3 m/s. He sees a huge crack in the sidewalk He sees a huge crack in the sidewalk and trips (spilling his pop). If the and trips (spilling his pop). If the time between when he saw the crack time between when he saw the crack and when he falls is 10 s. What was and when he falls is 10 s. What was his rate of acceleration? his rate of acceleration?

Calculating Acceleration when Calculating Acceleration when given a Displacementgiven a Displacement

vvff22 = v = vii

22 + 2a + 2a▲d▲d

vvii22 = v = vff

22 - - 2a2a▲d▲d

a = a = vvff22 – v – vii

22

2d2d

d = d = vvff22 – v – vii

22

2a2a

Sample Problem 1Sample Problem 1Justin is biking to the local swimming Justin is biking to the local swimming hole which is 20 km away. If he hole which is 20 km away. If he begins his trek traveling at a velocity begins his trek traveling at a velocity of 15 km/h and he accelerates at a of 15 km/h and he accelerates at a rate of 0.03m/srate of 0.03m/s22. What is Justin’s . What is Justin’s final velocity?final velocity?

Sample Problem 2Sample Problem 2Kerrin is moving at 1.8 m/s near the Kerrin is moving at 1.8 m/s near the top of a hill. 40 m later she is top of a hill. 40 m later she is traveling at 8.3 m/s. What is her traveling at 8.3 m/s. What is her average acceleration?average acceleration?

Sample Problem 3Sample Problem 3Lindsay is traveling to Moncton with Lindsay is traveling to Moncton with her friends to go shopping. If the car her friends to go shopping. If the car is initially traveling at a velocity of 45 is initially traveling at a velocity of 45 m/s for 100 km. When they reach m/s for 100 km. When they reach their destination they are traveling at their destination they are traveling at a velocity of 0 m/s, what is the rate a velocity of 0 m/s, what is the rate of acceleration?of acceleration?

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UNIT 1 MOTION. What do you think? If you walk from home to school, and then immediately return to your home. If the distance from your home to school