Acceleration =
Change in speed
Change in time
s
1
x
Plug in values
Clear the compound fraction
Final units
How we get units of m/s
2
50
m
s
s
50
m
s
50
m
s x s
50
m
s
2
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298
U
NIT
5
M
OTION
AND
F
ORCE
Calculating acceleration
The equation for
acceleration
To calculate acceleration, you divide the change in speed by the time
over which the speed changes. For example, if a bicycle’s speed
increases from 2 m/s to 6 m/s, its change in speed is 4 m/s. Because
two speeds are involved, subscripts are used to show the difference.
The starting speed is
v
1
, and the ending speed is
v
2
.
Positive and
negative
acceleration
If an object
speeds up
, it has a
positive acceleration
. If it
slows down
,
it has a
negative acceleration
. In physics, the word acceleration is
used to describe to any change in speed, positive or negative.
However, people sometimes use the word
deceleration
to describe the
motion that is slowing down.
ACCELERATION
Acceleration
(m/s
2
)
Change in speed
(m/s)
a
=
v
2

v
1
t
Time
(s)
Calculating
acceleration
A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 seconds (Figure 14.12). Calculate the acceleration.
1. Looking for:
You are asked for the acceleration in meters per second.
2. Given:
You are given the starting speed in m/s (
v
1
), final speed in m/s (
v
2
), and the time in seconds.
3. Relationships:
Use the formula for acceleration:
4. Solution:
Your turn...
a.
Calculate the acceleration of an airplane that starts at rest and reaches a speed of 45 m/s in 9 seconds.
Answer:
5 m/s
2
b.
Calculate the acceleration of a car that slows from 50 m/s to 30 m/s in 10 seconds.
Answer:
2 m/s
2
2
1
v
v
a
t
−
=
2
4 m/s
1 m/s
3 m/s
1 m/s
3 s
3 s
a
−
=
=
=
Figure 14.12:
An acceleration example
with a sailboat.