Change in VelocityChange in Velocity

Each time you take a Each time you take a step you are changing step you are changing the velocity of your body.the velocity of your body.

You are probably most You are probably most familiar with the velocity familiar with the velocity changes of a moving bus changes of a moving bus or car.or car.

The rate at which The rate at which velocity (speed or velocity (speed or direction) changes occur direction) changes occur is called acceleration.is called acceleration.

Acceleration= Acceleration= final velocity- starting final velocity- starting velocityvelocity

timetime

Change in velocity = final Change in velocity = final – – starting starting

velocity velocity velocity velocity

Acceleration= Acceleration= change in velocitychange in velocity

timetime

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph accelerates to90 mph in 3 seconds. What is thecar’s acceleration?

=90 mph - 60 mph

3 seconds

=30 mph

3 seconds

= 10 mph/second

PositivePositive acceleration acceleration

Negative Negative accelerationacceleration

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is thecar’s acceleration?

=0 mph - 60 mph

6 seconds

=- 60 mph

6 seconds

= - 10 miles per hour per second

- A constant - A constant acceleration acceleration

produces a straight produces a straight line or linear slope line or linear slope

(rise/run). (rise/run).

- The slope of a non-- The slope of a non-linear velocity-time linear velocity-time graph (rise/run) will graph (rise/run) will predict an objects predict an objects

instantaneous instantaneous acceleration. acceleration.

a = v/ta = v/t

Free fallFree fall The constant acceleration of The constant acceleration of

an object moving only under an object moving only under the force of gravity is "g". the force of gravity is "g".

The acceleration caused by The acceleration caused by gravity is 10 m/sgravity is 10 m/s22

If there was no air, all If there was no air, all objects would fall at the objects would fall at the same speedsame speed

Doesn’t depend on massDoesn’t depend on mass After 1 second falling at 10 After 1 second falling at 10

m/sm/s After 2 seconds 20 m/sAfter 2 seconds 20 m/s 3 seconds 30 m/s3 seconds 30 m/s

GalileoGalileo

1600’s 1600’s Studied how things Studied how things

fellfell Didn’t have a good Didn’t have a good

clockclock Rolled balls down an Rolled balls down an

inclined planeinclined plane Found that the speed Found that the speed

increased as it rolled increased as it rolled down the rampdown the ramp

GalileoGalileo

t = 0t = 1 second

t = 2 seconds

t = 3 seconds

Acceleration= Acceleration= change in change in velocityvelocity

timetime

GalileoGalileo

Same things happen when Same things happen when things fallthings fall Didn’t drop things from Tower of Pisa

vv22finalfinal = 2gd = 2gdyy

A final velocity can be A final velocity can be calculated over a vertical calculated over a vertical displacement “ddisplacement “dyy" during " during free fall using the free fall using the equation:equation:

ddyy = 1/2 gt = 1/2 gt22

The vertical displacement “dThe vertical displacement “dyy" that " that occurs during a specific time of free occurs during a specific time of free fall can be determined using the fall can be determined using the equation:equation:

Or a time interval can also be Or a time interval can also be determined over a specified determined over a specified distance of freefall using the distance of freefall using the equation:equation:

tt2 2 = 2d= 2dyy /g /g

FallingFalling Air resistance will Air resistance will

increase as it falls increase as it falls fasterfaster

An upward force on An upward force on the objectthe object

Eventually gravity Eventually gravity will balance with air will balance with air resistanceresistance

Reaches terminal Reaches terminal velocity - highest velocity - highest speed reached by a speed reached by a falling object.falling object.

Terminal velocityTerminal velocity Force of gravity is Force of gravity is

constantconstant air resistance increases as you speed up until the force is equal

Equal forces, no acceleration constant velocity terminal velocity