I.
Acceleration
A.
Acceleration = rate at which velocity changes
1)
Average Acceleration =
2)
v
a
t
change in velocit y
time to change
v  v2  v1
Initial velocity
New velocity
3)
a is vector quantity, so it requires a direction
4)
Units: velocity
time
m/s
 m / s / s  m / s2
s

distance/t ime d / t
d

 d /t /t  2
time
t
t
5)
B)
Instantaneous Acceleration = average acceleration over a short time,
where the acceleration is changing little
Direction of Acceleration
1) Deceleration is not a physics term; we call it negative acceleration
= acceleration in the direction opposite of the original velocity
2)
Acceleration of a car with constant speed
a) Any change in velocity is acceleration
b) Velocity = speed and direction
II.
Graphing Motion
A.
Distance versus Time Graph
1) Slope at any point = instantaneous velocity
change in position y
slope 

 velocity
change in time
x
2)
Example:
B.
Velocity versus Time Graph
1) Relationship to the Distance Graph
a) Straight line in Distance = Flat in Velocity
b) Slope change in Distance = change in Velocity
c) Negative slope in Distance = negative Velocity (going backward)
2)
Finding Acceleration form the Velocity Graph
y v
slope 

 acceleration
a) Acceleration = v/t
x t
b) Slope of the Velocity Graph = acceleration
c) Steep slope = large acceleration
d) Zero slope = no acceleration = no change in velocity
C.
Acceleration versus Time Graph
1) Spikes in the graph = v = acceleration
2)
The distance table doesn’t tell us how fast velocity changes, so we must
estimate the magnitude of the acceleration. We can tell the direction of
acceleration.
D.
Getting Distances from Velocity Graphs
1)
d
v
t
2)
d  vt
Distance = area of the shape under the Velocity Graph
III. Uniform Acceleration
A.
Uniform Acceleration = acceleration at a constant rate
1) Constant force acting on an object gives it uniform acceleration
2) Example: Gravity acts as a constant force on a falling object, so the
object accelerates at a constant rate
Uniform Acceleration
v is always increasing
No
Acceleration
v is constant
B.
Velocity During Uniform Acceleration
1) Velocity graph starting from rest
a) Slope is constant
b) Average velocity
vavg
2)
1
 vf
2
Velocity graph starting from an original velocity
a) vo = original velocity
b) at = v
v  v0  a t
vo
3)
Negative acceleration
v  v0  (a t )  v0  a t
0
-a
t
C.
Distance during uniform acceleration
1) Distance graph starting from rest
a)
1
d  v t  ( vf )t
2
a)
2)
vf  a t
1 2
d  at
2
Distance if the object was already moving
a)
d = (distance from original velocity) + (distance from unif. accel.)
1 2
d  (v0t )  ( a t )
2
b)
c)
d)
Graph of uniform acceleration when object already moving
Total area under the graph = distance traveled
Sample 2.3