This document discusses acceleration and how it relates to changes in an object's velocity over time. It defines acceleration as the rate of change of velocity, whether that means changing speed or direction. Acceleration is calculated by finding the change in velocity divided by the time taken. Positive acceleration increases velocity while negative acceleration decreases velocity. The constant acceleration due to gravity on Earth is approximately 10 m/s2. Free falling objects experience this acceleration and will fall at increasing speeds over time if air resistance is negligible. Galileo was one of the first scientists to study acceleration from gravity by rolling objects down inclined planes and observing their increasing speed over time.

2. Change in VelocityChange in Velocity
 Each time you take a step youEach time you take a step you
are changing the velocity ofare changing the velocity of
your body.your body.
 You are probably most familiarYou are probably most familiar
with the velocity changes of awith the velocity changes of a
moving bus or car.moving bus or car.
 The rate at which velocityThe rate at which velocity
(speed or direction) changes(speed or direction) changes
occur is called acceleration.occur is called acceleration.

3. Acceleration=Acceleration= final velocity- starting velocityfinal velocity- starting velocity
timetime
Change in velocity = finalChange in velocity = final
–– startingstarting
velocity velocityvelocity velocity
Acceleration=Acceleration= change in velocitychange in velocity
timetime

4. Acceleration =
Velocity(final) - Velocity(original)
time
A car traveling at 60 mph accelerates to
90 mph in 3 seconds. What is the
car’s acceleration?
=
90 mph - 60 mph
3 seconds
=
30 mph
3 seconds
= 10 mph/second

5. PositivePositive
accelerationacceleration
NegativeNegative
accelerationacceleration

6. 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 the
car’s acceleration?
=
0 mph - 60 mph
6 seconds
=
- 60 mph
6 seconds
= - 10 miles per hour per second

7. - A constant acceleration- A constant acceleration
produces a straight line orproduces a straight line or
linear slope (rise/run).linear slope (rise/run).
- The slope of a non-linear- The slope of a non-linear
velocity-time graphvelocity-time graph
(rise/run) will predict an(rise/run) will predict an
objects instantaneousobjects instantaneous
acceleration.acceleration.
a = v/ta = v/t

8. Free fallFree fall
 The constant acceleration of anThe constant acceleration of an
object moving only under theobject moving only under the
force of gravity is "g".force of gravity is "g".
 The acceleration caused byThe acceleration caused by
gravity is 10 m/sgravity is 10 m/s22
 If there was no air, all objectsIf there was no air, all objects
would fall at the same speedwould fall at the same speed
 Doesn’t depend on massDoesn’t depend on mass
 After 1 second falling at 10 m/sAfter 1 second falling at 10 m/s
 After 2 seconds 20 m/sAfter 2 seconds 20 m/s
 3 seconds 30 m/s3 seconds 30 m/s

9. GalileoGalileo
 1600’s1600’s
 Studied how things fellStudied how things fell
 Didn’t have a good clockDidn’t have a good clock
 Rolled balls down anRolled balls down an
inclined planeinclined plane
 Found that the speedFound that the speed
increased as it rolledincreased as it rolled
down the rampdown the ramp

10. GalileoGalileo
t = 0
t = 1 second
t = 2 seconds
t = 3 seconds
Acceleration=Acceleration= change in velocitychange in velocity
timetime

11. GalileoGalileo
Same things happen when things fallSame things happen when things fall
Didn’t drop things from Tower
of Pisa

12. vv22
finalfinal = 2gd= 2gdyy
 A final velocity can be calculatedA final velocity can be calculated
over a vertical displacement “dover a vertical displacement “dyy""
during free fall using the equation:during free fall using the equation:

13. ddyy = 1/2 gt= 1/2 gt22
 The vertical displacement “dThe vertical displacement “dyy" that" that
occurs during a specific time of free falloccurs during a specific time of free fall
can be determined using the equation:can be determined using the equation:
 Or a time interval can also beOr a time interval can also be
determined over a specified distancedetermined over a specified distance
of freefall using the equation:of freefall using the equation:
tt22
= 2d= 2dyy /g/g

14. FallingFalling
 Air resistance willAir resistance will
increase as it falls fasterincrease as it falls faster
 An upward force on theAn upward force on the
objectobject
 Eventually gravity willEventually gravity will
balance with airbalance with air
resistanceresistance
 Reaches terminal velocityReaches terminal velocity
- highest speed reached- highest speed reached
by a falling object.by a falling object.

15. Terminal velocityTerminal velocity
 Force of gravity is constantForce of gravity is constant
air resistance increases as
you speed up
until the force is equal
Equal forces, no
acceleration
constant velocity
terminal velocity