CPO Science
Foundations of Physics
Chapter 9
Unit 1, Chapter 4
Unit 1: Measurement and Motion
Chapter 4: Acceleration in a Straight Line
 4.1 Acceleration
 4.2 A Model for Accelerated Motion
 4.3 Free Fall and the Acceleration due
to Gravity
Chapter 4 Objectives
1. Calculate acceleration from the change is speed
and the change in time.
2. Give an example of motion with constant
acceleration.
3. Determine acceleration from the slope of the
speed versus time graph.
4. Calculate time, distance, acceleration or speed
when given three of the four variables.
5. Solve two-step accelerated motion problems.
6. Calculate height, speed, or time of flight in free
fall problems.
7. Explain how air resistance makes objects of
different masses fall with different accelerations.
Chapter 4 Vocabulary Terms







acceleration
m/sec2
delta D
constant acceleration
uniform acceleration
slope
term
 initial speed
 free fall
 acceleration due to
gravity (g)
 time of flight
 friction
 air resistance
 terminal speed
4.1 Acceleration
Key Question:
How is the speed of the ball changing?
*Students read Section 4.1 AFTER Investigation 4.1
4.1 Acceleration of a car
Acceleration is the rate of
change in the speed of an
object.
4.1 Acceleration vs. Speed
 Positive acceleration
and positive speed
4.1 Acceleration vs. Speed
 Negative acceleration
and positive speed
4.1 Acceleration
Acceleration
(m/sec2)
a = Dv
Dt
Change in speed (m/sec)
Change in time (sec)
4.1 Calculate Acceleration
 A student conducts an
 acceleration experiment by
coasting a bicycle down a
steep hill.
 The student records the speed
of the bicycle every second for
five seconds.
 Calculate the acceleration of
the bicycle.
4.1 Acceleration and Speed
 Constant acceleration is different from constant
speed.
 Motion with zero acceleration appears as a
straight horizontal line on a speed versus time
graph.
zero acceleration
constant speed
4.1 Acceleration and Speed
 Constant acceleration is sometimes called
uniform acceleration.
 A ball rolling down a straight ramp has constant
acceleration.
constant acceleration
increasing speed
4.1 Acceleration and Speed
 An object can have acceleration, but no speed.
 Consider a ball rolling up a ramp.
 As the ball slows down, eventually its speed
becomes zero.
constant negative
acceleration
decreasing speed
4.1 Slope and Acceleration
 Use slope to recognize when
there is acceleration in speed
vs. time graphs.
— Level sections (A) on the graph
show an acceleration of zero.
— The highest acceleration (B) is
the steepest slope on the
graph.
— Sections that slope down (C)
show negative acceleration
(slowing down).
4.2 A Model for Accelerated Motion
Key Question:
How do we describe and predict accelerated
motion?
*Students read Section 4.2 AFTER Investigation 4.2
4.2 Slope of a graph
 The slope of a graph is equal to
the ratio of rise to run.
 On the speed versus time
graph, the rise and run have
special meanings, as they did
for the distance versus time
graph.
 The rise is the amount the
speed changes.
 The run is the amount the time
changes.
4.2 Acceleration and slope
 Acceleration is the change in speed over the change in
time.
 The slope of the speed versus time graph is the
acceleration.
4.2 Calculate acceleration
 The following graph
shows the speed of a
bicyclist going over a
hill.
 Calculate the maximum
acceleration of the
cyclist and say when in
the trip it occurred.
4.2 Solving Motion Problems
4.2 Solving Motion Problems
4.2 Calculate speed
 A ball rolls at 2 m/sec onto
a ramp.
 The angle of the ramp
creates an acceleration of
0.75 m/sec2.
 Calculate the speed of the
ball 10 seconds after it
reaches the ramp.
4.2 Solving Motion Problems
initial position
distance if at constant speed
distance to add or subtract,
depending on acceleration
4.2 Calculate position
 A ball traveling at 2 m/sec rolls onto a ramp
that tilts upward.
 The angle of the ramp creates an
acceleration of -0.5 m/sec2.
 How far up the ramp does the ball get at its
highest point?
 (HINT: The ball keeps rolling upward until its
speed is zero.)
4.2 Solving Motion Problems
4.2 Calculate time
 A car at rest accelerates at 6 m/sec2.
 How long does it take to travel 440 meters
(about a quarter-mile) and how fast is the car
going at the end?
4.2 Calculate position
 A ball starts to roll down a ramp with
zero initial speed.
 After one second, the speed of the
ball is 2 m/sec.
 How long does the ramp need to be
so that the ball can roll for 3
seconds before reaching the end?
4.3 Solving Problems with Free Fall
4.3 Calculate height
 A stone is dropped down
a well and it takes 1.6
seconds to reach the
bottom.
 How deep is the well?
 You may assume the
initial speed of the stone
is zero.
4.3 Air Resistance and Mass
 The acceleration due to gravity does not
depend on the mass of the object which is
falling.
 Air creates friction that resists the motion of
objects moving through it.
 All of the formulas and examples discussed
in this section are exact only in a vacuum
(no air).
4.3 Terminal Speed
 You may safely assume that a = g =
9.8 m/sec2 for speeds up to several
meters per second.
 The resistance from air friction
increases as a falling object’s speed
increases.
 Eventually, the rate of acceleration is
reduced to zero and the object falls
with constant speed.
 The maximum speed at which an
object falls when limited by air
friction is called the terminal speed.
4.3 Free Fall and Acceleration due to
Gravity
Key Question:
How do you measure the acceleration of a falling
object?
*Students read Section 4.3 BEFORE Investigation 4.3
Application: Antilock Brakes