11-3
III. Acceleration
A. Acceleration- change in velocity divided by the time for
the change to occur (measure of how quickly velocity
changes)
1. Change in speed
a. When an object in motion speeds up, its
considered to be accelerating
1) Considered positive acceleration
b. Acceleration also occurs when an object slows down
because the speed has changed
1) sometimes known as deceleration
2) considered negative acceleration
c. Free fall- the movement of an object toward Earth
solely because of gravity.
1) The unit for velocity is meters per second (m/s)
2) The unit for acceleration then is meters per
second per second (m/s2)
3) Objects falling near Earth’s surface accelerate
downward at a rate of 9.8 m/s2
What Is Acceleration?
Each second an object is in
free fall, its velocity increases
downward by 9.8 meters per
second.
The change in the stone’s
speed is 9.8 m/s2, the
acceleration due to gravity.
t=0s
v = 0 m/s
t=1s
v = 9.8 m/s
t=2s
v = 19.6 m/s
t=3s
v = 29.4 m/s
2. acceleration also occurs when an object is turning
/changing direction
a. even if an object is traveling at a constant speed, it
can still be accelerating if it is changing direction
3. Changes in speed and direction
a. Sometimes motion can have both speed and
direction at the same time.
1) Passengers in a car moving along a winding
road experience rapidly changing acceleration.
The car can slow down going around a long
winding curve.
What Is Acceleration?
A roller coaster produces acceleration due to changes
in both speed and direction.
4. Constant Acceleration- a steady change in velocity
a. The velocity of an object moving in a straight line
changes at a constant rate when the object is
experiencing constant acceleration.
1) An airplane’s acceleration may be constant
during a portion of its takeoff.
What Is Acceleration?
Constant acceleration during take off results in
changes to an aircraft’s velocity that is in a constant
direction.
B. Acceleration can be calculated for an object in a straight
line if you know how an object’s velocity has changed
during a given time period.
1. formula- acceleration = final velocity – initial
velocity ÷ time
v f  vi
t
a. when an object speeds up, the final speed is
always greater than the initial speed- “positive
acceleration”
b. when an object slows, the final speed is less than
the initial speed- “negative acceleration”
2. units- meters per second squared (m/s2), (km/hr2),
(mi/hr2), (cm/s2)
a. A ball rolls down a ramp, starting from rest. After
2 seconds, its velocity is 6 meters per second.
What is the acceleration of the ball?
v
a
t
v= 6 m s  0 m s
a= ?
t= 2s
6m 0m
s
s
2s
 3m
s2
b. Calculate an airplane who’s speed changes from
40 m/s to 0 m/s in 5 seconds. What is its average
acceleration?
v
a
t
v= 0 m s  40 m s
a= ?
t= 5s
0 m  40 m
s
s
5s
40 m
5s
s  8 m
s2
C. Graphing Acceleration
1. Speed-versus-Time Graph
a. Constant acceleration is represented on a speedtime graph by a straight line
b. The slope of a line is the acceleration
c. The graph is an example of a linear graph, in
which the displayed data form straight-line parts.
d. If a line slants upward, the graph shows that your
speed is increasing (positive acceleration)
Graphs of Accelerated Motion
The skier’s acceleration is positive. The
acceleration is 4 m/s2.
e. If a line slopes downward, its speed is decelerating
(negative acceleration)
f. If there is a straight line across, there is no
acceleration (the speed is constant)
Graphs of Accelerated Motion
The biker moves at a constant speed and then slows to
a stop.
2. Distance-versus-time graph
a. Accelerated motion is represented by a curved line
on a distance-time graph.
b. In a nonlinear graph, a curve connects the data
points that are plotted
c. A curved line means the object is accelerating
1) A curved line shows that for each second you
traveled a greater distance than the second
before.
d. Since the line is increasing so is your speed.
Graphs of Accelerated Motion
A distance-time graph of accelerated motion is a
curve. The data in this graph are for a ball dropped
from rest toward the ground.
Graphs of Accelerated Motion
Compare the slope of the curve during the first second
to the slope during the fourth second. An increasing
slope means that the speed is increasing.
D. Instantaneous Acceleration- how fast a velocity is
changing at a specific instant.
1. Acceleration is rarely constant, and motion is rarely in
a straight line
a. Acceleration involves a change in velocity or
direction or both, so the vector of acceleration can
point in any direction.
b. The vector’s length depends on how fast velocity
is changing.
c. For an object that is standing still, the acceleration
vector is zero.