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
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.