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Physics of Motion. 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 moved from here we have had some kind of motion. What is the difference between speed and acceleration?

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Physics of motion1
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 moved from here we have had some kind of motion.


Physics of motion

What is the difference between speed and acceleration?

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


Speed
Speed

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

  • It’s one example of a rate.

  • Speed is a distance divided by a time

    S = D/ T


Units
UNITS

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

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

    cm/sec, light years/century etc.





Check for understanding
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
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 vs constant speed
Instantaneous vs. Average Speed vs. Constant Speed

  • Instantaneous speed is speed at a particular instant

  • Constant speed never changes

  • Average speed is total distance covered for a trip divided by total time elapsed

    average speed = total distance/time


Check for understanding1
Check for Understanding

  • What is the difference between instantaneous and average speed?


Examples
Examples

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

    S = distance/time = D/T =

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


What s unknown
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 trick
Memory Trick

  • D = S x T

  • S = D/T

  • T = D/S

D

S

T

When solving problems, always write the symbolic equation first


Remember your algebra
Remember your Algebra

  • S = D/T ; multiply both sides by T

  • S x T = D

  • D = S x T; divide both sides by S

  • D/S = T

  • T = D/S

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


Distance unknown
Distance Unknown

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

  • D = S x T=18 m/s x 60 sec =1080 m

  • Try another one; How far can Sarah run if she averages 4.5 m/s for three minutes and 20 seconds? (What are we going to write first?)

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


Question
Question

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

  • T = D/S

  • T = 200 cm/ 1.0 cm/s

  • T = 200 s

  • T = 3 minutes 20 seconds


Word problem practice
Word Problem Practice

  • Write a symbolic equation for this sentence:

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

  • Now write in the numbers

  • Now find the answer


Check for understanding2
Check for understanding

  • Does a speedometer measure average speed or instantaneous speed?

Courtesy of CobraCountry.com


Unit conversion
Unit Conversion

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

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

  • This is called the factor-label method

90 km/hr


You try it
You Try It

  • Convert 125.0 km/hr to meters/sec

  • 125.0 km/hr x 1000m/1 km x 1 hr/3600 sec =

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

34.7 m/s


Velocity
Velocity

  • Velocity is speed in a given direction

  • Constant velocity requires both constant speed and constant direction

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

  • NO! It’s direction is continually changing.



Acceleration1
Acceleration

  • How fast velocity changes

  • Acceleration = change of velocity/time

  • Includes increases and decreases of speed and changes in direction

  • Acceleration (+) Deceleration (-)

  • a= Vf- Vi/ t

  • Acceleration = a Time = t

  • Vf = Final Velocity Vi= Initial Velocity


Acceleration equations
Acceleration Equations

a= Vf-Vi/t

t = Vf-Vi/a

Vf = (a x t) + Vi

Vi = Vf – (a x t)

UNITS MUST MATCH!


Finding acceleration
Finding Acceleration

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

    Answer: 5 km/h/s

  • In 10 seconds a train increases speed from 20 km/h to 40 km/h. What is its acceleration?

  • a = 20km/h ÷ 10s = 2.0 km/h/s


Free fall
Free Fall

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

  • v= gt = 9.8t

  • g = 9.8 m/s/s

  • g = 9.8 m/s2


More on free fall
More on Free Fall

  • Due to gravity a = 9.8 m/s2= g

  • v = gt

  • Instantaneous speed = acceleration x time

  • Question: What is the speed of a rock that has fallen from rest for 5.5 seconds? (without air resistance)


Galileo s experiment
Galileo’s Experiment

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

Courtesy Dan Heller Photography


Rising and falling rock
Rising and Falling Rock

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

  • 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 fallen
Distance Fallen

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

  • What is distance fallen in this time?

  • What is average speed during second second of fall?

  • What is distance fallen in second second?

  • What is distance fallen in first two 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 pattern
The Pattern

  • Distance fallen in t seconds

    d = 1/2gt2

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

    d= vit + 1/2gt2


Falling apple
Falling Apple

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

  • What is its speed when it hits?

  • What is its average speed?

  • How high did it fall from?


Free fall problem
Free Fall Problem

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


Helicopter problems
Helicopter Problems

1. A Helicopter is rising 5.0 m/s and someone drops a bag from it. After two seconds, what is the bags velocity, how far has the bag fallen and how far below the helicopter is the bag?

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


Weather balloon problem
Weather Balloon Problem

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

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

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


Air resistance
Air Resistance

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

  • What would happen on the moon?


Confused
Confused?

  • Explain the difference between velocity and acceleration and velocity?

  • Is acceleration an example of a velocity?

  • Can an object with zero velocity be accelerating?

  • At the top of its path, the velocity of a rock thrown upward is ________?

  • At the top, its acceleration is _______?