1. Acceleration
When an object moves, most of the time it’s motion (velocity) will not be constant.
Whenever an object changes it’s velocity (speed with a direction) the object has what is called an acceleration.
An object has an acceleration whenever it…
Speeds up
Slows down
Changes direction
An acceleration is how fast the velocity of an object changes.
Since velocity is a vector, acceleration is also a vector.

2. Instantaneous and Average Acceleration
There are two types of acceleration:
Average acceleration– This is how fast an object
changes it’s velocity over a
period of time.
Instantaneous acceleration– How fast an object changes
it’s velocity at a given point in time.
A car drives speeds up from 0 to 50 MPH in 5 seconds.
This takes place in 5 seconds time so this is an average.
This is an average acceleration
A rock is dropped, and accelerates downward at 9.8 m/s/s when released.
The rock accelerates at 9.8 m/s/s at THE INSTANT it is released.
This is an instantaneous acceleration.

3. Calculating Average Acceleration
Acceleration is how fast the velocity changes.
It is the change in velocity in a given time.
Change in Velocity
Average Acceleration =
Time for the change
The Units for acceleration can
be any unit of velocity (speed)
divided by a unit of time.
Units for Acc:
(Meters/sec)/sec or Meters/sec2
(Miles/Hr.)/sec
(Feet/min)/sec
(Kilometers/Hr.)/min
Acc.
Time
Vf -Vi

4. Using the acceleration box to find the average acceleration
A Girl starts from rest and accelerates to a running speed of 8 m/s in a time of .5 seconds. What is her average acceleration?
Next cover up the part of the
box you are looking for.
The equation you want is:
Vf - Vi
Acc =
Time
Acc.
Vf -Vi
Finally substitute the numbers into the
equation and solve.
Vf -Vi
Acc =
Time
8 m/s – 0 m/s
Acc = = 16 m/s/s or 16 m/s2
.5 sec
Acc.
First write out the box
Acc.
Time
Vf -Vi

5. Using the acceleration box to find the time needed to accelerate
A car traveling at 6 m/s accelerates at a rate of 4m/s2. How much time will it take to reach a speed of 14 m/s?
Finally substitute the numbers into the
equation and solve.
Vf -Vi
Time =
Acc
14 m/s – 6 m/s m/s
Time = = = 2 sec
4 m/s m/s2
Acc.
Time
Next cover up the part of the
box you are looking for.
The equation you want is:
Vf - Vi
Time =
Acc
Acc.
Time
Vf -Vi
First write out the box
Acc.
Time
Vf -Vi

6. Using the acceleration box to find the final velocity (speed).
A rock is dropped and falls with a constant acceleration of –9.8 m/s2. What will the rock’s velocity be 5 seconds into the fall?
Finally substitute the numbers into the
equation and solve.
Vf = Acc*Time + Vi
Vf = -9.8 m/s2 * 5 s + 0 m/s
Vf = - 49 m/s ( - means DOWN)
Acc.
Time
Vf -Vi
Next cover up the part of the
box you are looking for.
The equation you want is:
Vf – Vi = Acc. * Time
which becomes
Vf = Acc*Time + Vi
Acc.
Time
Vf -Vi
First write out the box
Acc.
Time
Vf -Vi

7. Using the acceleration box to find the Initial velocity (speed).
A ball is rolled across a floor with with an unknown speed, and comes to a complete stop in
5 seconds. If the acceleration of the ball is m/s2, what was the initial speed of the ball?
Finally substitute the numbers into the
equation and solve.
Vi = -(Acc*Time + Vf)
Vi = -(-.5 m/s2 * 5 s + 0 m/s)
Vi = m/s2
Acc.
Time
Vf -Vi
Next cover up the part of the
box you are looking for.
The equation you want is:
Vf – Vi = Acc. * Time
which becomes
- Vi = Acc*Time – Vf
Multiply both sides by –1
Vi = -(Acc*Time – Vf)
Acc.
Time
Vf -Vi
First write out the box
Acc.
Time
Vf -Vi

8. Picturing Acceleration
Let us say that there is a ball that rolls from rest with a constant acceleration of 2m/s2. What would the ball’s motion look like second by second?
0 m
.5m
2 m
4.5 m
8 m

9. Graphing the Displacement of Acceleration
We can construct a data table and a position verse time graph for the motion.
Position
(m)
Time (sec)
Time
(seconds)
Position
(meters) 1 2 3 4 .5
4.5 8
The position verses time graph for accelerated
motion will ALWAYS be a parabola. The is because the
velocity (the slope) is always changing.

10. Speeding Up, Slowing Down
If you are speeding up parabola becomes more curved. That is because
the distance traveled each second increases more and more.
Position
(m)
Time (sec)
Moving in a positive direction
Position
(m)
Time (sec)
Moving in a negative direction
If you are slowing down the parabola becomes less curved. That is
because the distance traveled each second becomes less and less.
Position
(m)
Time (sec)
Moving in a negative direction
Position
(m)
Time (sec)
Moving in a positive direction

11. Graphing the Velocity of an Accelerated Object
Vf -Vi
Acc =
Time
Let’s start with the acceleration equation
We can rewrite the acceleration equation
Vf = acc*time + Vi
Now compare it to
The equation for a straight
line
y = m*x + b
They are the same!!!
Y = Vf
M = slope = acceleration
B = intercept = Vi

12. Graphing the Velocity of an Accelerated Object
This means that the velocity graph for a object moving with a constant acceleration is a straight line. THE SLOPE OF THE LINE, IS THE ACCLERATION!!!!
time
Vel.
A positive slope means a
positive acceleration.
time
Vel.
A negative slope means a
negative acceleration.

13. Remember +/- means direction
An object can have a negative
acceleration and still pick up
speed. If the object already
has a negative velocity. V t
An object can have a positive
acceleration and slow down.
If the object started with a
negative velocity. V t
Important note: If the velocity line moves away from the
time (X) axis the object is speeding up. If the velocity line
moves to the time (X) axis the object is slowing down.