Physics of Motion. Frame of Reference- background or object that shows a change in position. Ex. Earth or the Horizon Fixed in place. If an object is

Physics of MotionPhysics of Motion

Physics of MotionPhysics of Motion

Frame of Reference- background or Frame of Reference- background or object that shows a change in object that shows a change in position.position.

Ex. Earth or the HorizonEx. Earth or the Horizon

Fixed in place. If an object is moved Fixed in place. If an object is moved from here we have had some kind of from here we have had some kind of motion.motion.

What is the difference between speed and acceleration?

Can a car be speeding very fast and have zero acceleration?

SpeedSpeed

Speed is a measure of how much Speed is a measure of how much distance is covered in a given distance is covered in a given amount of time.amount of time.

It’s one example of a It’s one example of a rate.rate. Speed is a distance divided by a timeSpeed is a distance divided by a time

S = D/ TS = D/ T

UNITSUNITS

Any distance unit Any distance unit and any time unit and any time unit can be used to can be used to define a speeddefine a speed

Examples km/hr, Examples km/hr, meters/sec, mi/hr,meters/sec, mi/hr,

cm/sec, light cm/sec, light years/century etc.years/century etc.

Comparing UnitsComparing Units

20 km/h20 km/h 12 mi/h12 mi/h 6 m/s6 m/s






200 km/h200 km/h ?? ??








200 km/h200 km/h 120 mi/h120 mi/h ??









Check for Understanding

On your team’s whiteboard, write an equation and solve for the average speed when Betty swims 50.0 meters in 27.4 seconds. Be sure to use correct units and state your answer in two or three significant figures.

S = D/T = 50.0m/27.4 s = 1.82 m/s

Car Trip

D = 1.22 m T = 1.13 s 1.37 s Use T = 1.25s S = D/T = 1.22m / 1.25 s = 0.976

m/s = 0.98 m/s = 1.0 m/s

Instantaneous vs. Average Speed Instantaneous vs. Average Speed vs. Constant Speedvs. Constant Speed

Instantaneous speed is speed at a Instantaneous speed is speed at a particular instantparticular instant

Constant speed never changesConstant speed never changes Average speed is total distance Average speed is total distance

covered for a trip divided by total covered for a trip divided by total time elapsedtime elapsed

average speed = total average speed = total distance/timedistance/time

Check for UnderstandingCheck for Understanding

What is the difference between What is the difference between instantaneous and average speed?instantaneous and average speed?

ExamplesExamples

Find the average speed of a car trip Find the average speed of a car trip covering 480 km in 6.0 hrs (be sure covering 480 km in 6.0 hrs (be sure to write the symbolic equation first)to write the symbolic equation first)

S = distance/time = D/T = S = distance/time = D/T =

480 km/ 6.0 h = 80. km/h (note that 480 km/ 6.0 h = 80. km/h (note that it’s two significant figures)it’s two significant figures)

What’s Unknown?

Start with S = D/T and find an equation for

D = and an Equation for T =

S x T

D/S

Memory TrickMemory Trick

D = S x TD = S x T

S = D/TS = D/T

T = D/ST = D/S

D

S TWhen solving problems, always write the symbolic equation first

Remember your AlgebraRemember your Algebra

S = D/T ; multiply both sides by TS = D/T ; multiply both sides by T S x T = DS x T = D D = S x T; divide both sides by SD = S x T; divide both sides by S D/S = TD/S = T T = D/ST = D/S

When solving problems, always write the symbolic equation first. Then an equal sign, then put in the known numbers, then solve.

Distance UnknownDistance Unknown

Find the distance covered by a horse Find the distance covered by a horse running 18 m/s for one minuterunning 18 m/s for one minute

D = S D = S xx T=18 m/s T=18 m/s x x 60 sec60 sec =1080 m =1080 m Try another one; How far can Sarah run if Try another one; How far can Sarah run if

she averages 4.5 m/s for three minutes she averages 4.5 m/s for three minutes and 20 seconds? (What are we going to and 20 seconds? (What are we going to write first?)write first?)

D = S D = S xx T = 4.5 m/s T = 4.5 m/s x x 3.0 min 3.0 min x x 60s/ 60s/ 1minute = 810 m1minute = 810 m

QuestionQuestion

How long does it take a snail How long does it take a snail creeping at 1.0 cm per second to creeping at 1.0 cm per second to cross a 2.0 meter walkway?cross a 2.0 meter walkway?

T = D/ST = D/S T = 200 cm/ 1.0 cm/sT = 200 cm/ 1.0 cm/s T = 200 sT = 200 s T = 3 minutes 20 seconds T = 3 minutes 20 seconds

Word Problem PracticeWord Problem Practice

Write a symbolic equation for this Write a symbolic equation for this sentence:sentence:

How long does it take for the How long does it take for the Metroliner train to go from NY to Metroliner train to go from NY to Boston, which are 520 km apart, if it Boston, which are 520 km apart, if it averages 127 km/hr?averages 127 km/hr?

Now write in the numbersNow write in the numbers

Now find the answerNow find the answer

Check for understandingCheck for understanding

Does a speedometer measure Does a speedometer measure average speed or instantaneous average speed or instantaneous speed?speed?

Courtesy of CobraCountry.com

Unit ConversionUnit Conversion

Suppose we want to convert 25 m/s Suppose we want to convert 25 m/s to km/hourto km/hour

25 m/s x 1 km/1000m x 3600s/1 hour 25 m/s x 1 km/1000m x 3600s/1 hour = =

This is called the factor-label methodThis is called the factor-label method

90 km/hr

You Try ItYou Try It

Convert 125.0 km/hr to meters/secConvert 125.0 km/hr to meters/sec 125.0 km/hr x 1000m/1 km x 1 125.0 km/hr x 1000m/1 km x 1

hr/3600 sec = hr/3600 sec =

Another word for the “labels” in this Another word for the “labels” in this method would be the ???method would be the ???

34.7 m/s

VelocityVelocity Velocity is speed in a Velocity is speed in a

given directiongiven direction Constant velocity Constant velocity

requires requires bothboth constant constant speed and constant speed and constant directiondirection

Is a car traveling on a Is a car traveling on a circular track at circular track at steady speed moving steady speed moving at constant velocity?at constant velocity?

NO! It’s direction is NO! It’s direction is continually changing.continually changing.

AccelerationAcceleration

AccelerationAcceleration

How fast How fast velocityvelocity changes changes Acceleration = change of velocity/timeAcceleration = change of velocity/time Includes increases and decreases of Includes increases and decreases of

speed and changes in directionspeed and changes in direction Acceleration (+) Deceleration (-)Acceleration (+) Deceleration (-) a= Vf- Vi/ ta= Vf- Vi/ t Acceleration = a Time = tAcceleration = a Time = t Vf = Final Velocity Vi= Initial VelocityVf = Final Velocity Vi= Initial Velocity

Acceleration EquationsAcceleration Equations

a= Vf-Vi/ta= Vf-Vi/t t = Vf-Vi/at = Vf-Vi/a Vf = (a x t) + ViVf = (a x t) + Vi Vi = Vf – (a x t)Vi = Vf – (a x t)

UNITS MUST MATCH!UNITS MUST MATCH!

Finding AccelerationFinding Acceleration

A car steadily increases its speed A car steadily increases its speed each second from 35 to 40 to 45 each second from 35 to 40 to 45 km/h. What is its acceleration?km/h. What is its acceleration?

Answer: 5 km/h/sAnswer: 5 km/h/s In 10 seconds a train increases speed In 10 seconds a train increases speed

from 20 km/h to 40 km/h. What is its from 20 km/h to 40 km/h. What is its acceleration?acceleration?

a = 20km/h a = 20km/h ÷ 10s = 2.0 km/h/s÷ 10s = 2.0 km/h/s

Free FallFree Fall

In free fall an In free fall an object’s speed object’s speed increases by about increases by about 10 m/s in each 10 m/s in each second. second.

v = gt = 9.8tv = gt = 9.8t

g = 9.8 m/s/sg = 9.8 m/s/s g = 9.8 m/sg = 9.8 m/s22

Time to Time to fall(s)fall(s)

Speed Speed (m/s)(m/s)

00 00

11 9.89.8

22 19.619.6

33 29.429.4

44 39.239.2

55 4949

More on Free FallMore on Free Fall

Due to gravity a = 9.8 m/sDue to gravity a = 9.8 m/s22= g= g v = gtv = gt Instantaneous speed = acceleration Instantaneous speed = acceleration

x timex time Question: What is the speed of a Question: What is the speed of a

rock that has fallen from rest for 5.5 rock that has fallen from rest for 5.5 seconds? (without air resistance)seconds? (without air resistance)

Galileo’s ExperimentGalileo’s Experiment

Which would reach Which would reach the ground first, a the ground first, a marble or a marble or a cannonball?cannonball?

Courtesy Dan Heller Photography

Rising and Falling RockRising and Falling Rock

A rock is thrown upward with 20 m/s. A rock is thrown upward with 20 m/s. It rises then falls to the height from It rises then falls to the height from which thrown. What will be its speed which thrown. What will be its speed at that height? It’s velocity?at that height? It’s velocity?

Answer 20 m/s (down)Answer 20 m/s (down)

Gravity takes speed away on the way up at 9.8 m/s/s and then gives it back on the way down, at the same rate

Distance FallenDistance Fallen

What is average speed of an object that What is average speed of an object that falls for 1 second? falls for 1 second?

What is distance fallen in this time?What is distance fallen in this time?

What is average speed during second What is average speed during second second of fall? second of fall?

What is distance fallen in second second?What is distance fallen in second second?

What is distance fallen in first two What is distance fallen in first two seconds?seconds?

5 m/s, average of 0 and 10

5m = 5 m/s x 1s

15 m/s, average of 10 and 20

15m = 15m/s x 1s

20m = 5m + 15m

The PatternThe Pattern

Distance fallen in t Distance fallen in t secondsseconds

d = 1/2gtd = 1/2gt22

Now if the object is in Now if the object is in motion, then you have motion, then you have to account for that as to account for that as well. well.

d= vd= viit + 1/2gtt + 1/2gt22

timetime distancedistance

11 55

22 2020

33 4545

44 8080

55 125125

Falling AppleFalling Apple

An apple drops from the tree and hits An apple drops from the tree and hits the ground in two secondsthe ground in two seconds

What is its speed when it hits? What is its speed when it hits? What is its average speed?What is its average speed? How high did it fall from?How high did it fall from?

Free Fall ProblemFree Fall Problem

A person is standing on top of a roof, A person is standing on top of a roof, holding two objects. The person drops holding two objects. The person drops item A and at the same time throws item A and at the same time throws item b straight up over the edge of the item b straight up over the edge of the building with an initial speed of 25 m/s. building with an initial speed of 25 m/s. If the building itself is 450 m high, how If the building itself is 450 m high, how long will it take both objects to hit the long will it take both objects to hit the ground and at what speed will they hit ground and at what speed will they hit the ground with?the ground with?

Helicopter ProblemsHelicopter Problems 1. A Helicopter is rising 5.0 m/s and 1. A Helicopter is rising 5.0 m/s and

someone drops a bag from it. After someone drops a bag from it. After two seconds, what is the bags two seconds, what is the bags velocity, how far has the bag fallen velocity, how far has the bag fallen and how far below the helicopter is and how far below the helicopter is the bag?the bag?

2. The helicopter in problem one 2. The helicopter in problem one now descends 5.0 m/s. After two now descends 5.0 m/s. After two seconds, what is the bags velocity, seconds, what is the bags velocity, how far has the bag fallen and how how far has the bag fallen and how far below the helicopter is the bag?far below the helicopter is the bag?

Weather Balloon ProblemWeather Balloon Problem

A weather balloon is floating upward A weather balloon is floating upward at 2.5 m/s above the Earth when it at 2.5 m/s above the Earth when it releases a pack of instruments.releases a pack of instruments.

A. If the pack hits the ground with a A. If the pack hits the ground with a velocity of 73.5 m/s how far did the velocity of 73.5 m/s how far did the pack fall?pack fall?

B. How long did it take for the pack B. How long did it take for the pack to fall?to fall?

Air ResistanceAir Resistance

Why, on earth, Why, on earth, does a coin reach does a coin reach the ground faster the ground faster than a feather?than a feather?

What would What would happen on the happen on the moon?moon?

Confused?Confused?

Explain the difference between velocity Explain the difference between velocity and acceleration and velocity?and acceleration and velocity?

Is acceleration an example of a velocity?Is acceleration an example of a velocity? Can an object with zero velocity be Can an object with zero velocity be

accelerating?accelerating? At the top of its path, the velocity of a rock At the top of its path, the velocity of a rock

thrown upward is ________?thrown upward is ________? At the top, its acceleration is _______?At the top, its acceleration is _______?

Documents

Physics of Motion. Frame of Reference- background or object that shows a change in position. Ex. Earth or the Horizon Fixed in place. If an object is