Acceleration
Assessment
Velocity vs. time
5. The motion of a particle
along a straight line is
depicted in this graph.
What is the acceleration of
the particle from 7 seconds
to 10 seconds?
V
(m/s)
t (s)
Examples
An accelerating object has a changing
velocity.
a coaster making a turn
a ball rolling uphill
a baseball falling
What is acceleration?
4 m/s
4 m/s
4 m/s
4 m/s
0 m/s
2 m/s
4 m/s
2
6 m/s
Two balls are moving to
the right. Their velocity
at each second is shown.
•
Which ball is
accelerating?
•
What is its
acceleration?
What is acceleration?
4 m/s
4 m/s
4 m/s
4 m/s
0 m/s
2 m/s
4 m/s
Two balls are moving to
the right. Their velocity
at each second is shown.
•
Which ball is
accelerating?
•
What is its
acceleration?
Ball 2 is accelerating at
+2 m/s per second:
2
6 m/s
a = +2 m/s2
Units of acceleration
The acceleration tells you how many meters per
second your velocity changes in each second.
These units are usually written as meters per second squared.
Exploring the ideas
Click on this
interactive
calculator on
page 110.
Signs of the acceleration
Positive acceleration of +4 m/s2 adds +4 m/s of velocity each second.
0 m/s 4 m/s
8 m/s
12 m/s
16 m/s
Negative acceleration of -4 m/s2 adds -4 m/s of velocity each second.
16 m/s
12 m/s
8 m/s
4 m/s
0 m/s
Test your knowledge
A car is headed west (the negative direction) on a long
straight road. The driver sees a red light up ahead and
slows to a stop.
Is the car’s acceleration positive or negative?
Test your knowledge
A car is headed west (the negative direction) on a long
straight road. The driver sees a red light up ahead and
slows to a stop.
Is the car’s acceleration positive or negative?
Slowing down in the
negative direction is +a!
Acceleration on
the v vs. t graph
1.
A car moves at a constant
speed of 3 m/s for 3 seconds.
2.
The car accelerates to 6 m/s
over the next 3 seconds.
3.
The car continues at 6 m/s for
three more seconds.
What does this look like?
No
No
Positive
acceleration acceleration acceleration
constant
velocity
changing
velocity
constant
velocity
Position vs. time
An object starting from rest
accelerates at 1 m/s2.
Its velocity increases with time,
making a linear v vs. t graph.
What does the position vs. time
graph look like?
• As the velocity increases the
slope must change!
The graph is a curve.
Curves vs. lines
Acceleration creates a sloped line on a v vs. t graph.
Acceleration creates a curve on an x vs. t graph.
Assessment
A car changes its velocity from 0 to 20 m/s in
4.0 seconds. What is its acceleration?
Assessment
A car changes its velocity from 0 to 20 m/s in
4.0 seconds. What is its acceleration?
A change of +20 m/s over 4.0 seconds is an
acceleration of +5.0 m/s2.
Gravity and
free fall
What is free fall?
An object is in free fall whenever it moves solely under
the influence of gravity, regardless of its direction.
A ball falling down,
with negligible air
resistance
A ball thrown up,
with negligible
air resistance
A ball launched at ANY
angle, as long as there is
negligible air resistance
Gravity and free fall
Near Earth’s surface, free-falling objects
have a downward acceleration of 9.8 m/s2.
If an object is dropped from rest, then . . .
• after 1 second its velocity is -9.8 m/s.
• after 2 seconds its velocity is -19.6 m/s.
• after 3 seconds its velocity is -29.4 m/s.
• after 10 seconds its velocity is -98 m/s.
Describe free fall with equations
The free fall equations are identical to the equations
for motion with constant acceleration:
The only difference is that you already know the acceleration
because it is always 9.8 m/s2 downward.
Find your reaction time
Use this equation for free fall to find
your own reaction time—the time to
catch a falling ruler.
Make a prediction first:
Will your reaction time be in
seconds? Tenths of a second?
Hundredths of a second?
Gravity and free fall
Do falling objects REALLY keep
moving faster and faster?
No! In real life there is air resistance.
As falling objects speed up, the force
of air resistance increases.
When the air resistance gets as strong
as the force of gravity, the falling
object stops accelerating.
Terminal velocity
Most objects reach this terminal
velocity within a few seconds of
being dropped.
Terminal velocity is the final
maximum velocity an object reaches
because of air resistance.
A falling human has a terminal
velocity of about 140 miles per hour
(or about 60 m/s).
When can motion be
treated as free fall?
Free fall is a very good approximation for solid,
dense objects dropped from ten meters or so.
For these situations, air resistance can be ignored.
The symbol g is often used when the acceleration
of an object is due only to gravity.
Example free fall problem
From what height should you drop a ball if you want
it to hit the ground in exactly 1.0 second?
Asked: x
Given: t
v0
Relationship:
Solution:
Example free fall problem
From what height should you drop a ball if you want
it to hit the ground in exactly 1.0 second?
Asked: x
Given: t = 1.0 s, g = -9.8 m/s2
(assume v0 = 0 m/s and x0 = 0 m)
Relationship:
Solution:
Example free fall problem
From what height should you drop a ball if you want
it to hit the ground in exactly 1.0 second?
Asked: x
Given: t = 1.0 s, g = -9.8 m/s2
(assume v0 = 0 m/s and x0 = 0 m)
Relationship:
Solution:
Example free fall problem
From what height should you drop a ball if you want
it to hit the ground in exactly 1.0 second?
Asked: x
Given: t = 1.0 s, g = -9.8 m/s2
(assume v0 = 0 m/s and x0 = 0 m)
Relationship:
Solution:
Example free fall problem
From what height should you drop a ball if you want
it to hit the ground in exactly 1.0 second?
Asked: x
Given: t = 1.0 s, g = -9.8 m/s2
(assume v0 = 0 m/s and x0 = 0 m)
Relationship:
Solution:
The negative sign means that the final position
is 4.9 m below the initial position.
4.9 m
high
Assessment
A ball is thrown straight upward at 15 m/s.
a) How long does it take to reach its highest point?
b) What height does it reach, assuming it started at zero height?
Assessment
A ball is thrown straight upward at 15 m/s.
a) How long does it take to reach its highest point?
asked: time
given: v0 = 15 m/s, v = 0 m/s, a = g = -9.8 m/s2
relationship:
solution: