1. 4.1 Acceleration 1

2. Chapter Objectives
Calculate acceleration from the change in speed and the change in time.
Give an example of motion with constant acceleration.
Determine acceleration from the slope of the speed versus time graph.
Calculate time, distance, acceleration, or speed when given three of the four values.
Solve two-step accelerated motion problems.
Calculate height, speed, or time of flight in free fall problems.
Explain how air resistance makes objects of different masses fall with different accelerations.

3. Chapter Vocabulary acceleration acceleration due to gravity (g)
air resistance
constant acceleration
delta (Δ)
free fall
initial speed
m/s2
term
terminal velocity
time of flight
uniform acceleration

4. Inv 4.1 Acceleration Investigation Key Question:
How does acceleration relate to velocity? 4

5. 4.1 Acceleration
Acceleration is the rate of change in the speed of an object.
Rate of change means the ratio of the amount of change divided by how much time the change takes.

6. 4.1 Acceleration in metric units
If a car’s speed increases from 8.9 m/s to 27 m/s, the acceleration in metric units is 18.1 m/s divided by 4 seconds, or 4.5 meters per second per second.
Meters per second per second is usually written as meters per second squared (m/s2).

7. 4.1 The difference between velocity and acceleration
Velocity is fundamentally different from acceleration.
Velocity can be positive or negative and is the rate at which an object’s position changes.
Acceleration is the rate at which velocity changes.

8. 4.1 The difference between velocity and acceleration
The acceleration of an object can be in the same direction as its velocity or in the opposite direction.
Velocity increases when acceleration is in the same direction.

9. 4.1 The difference between velocity and acceleration
When acceleration and velocity have the opposite sign the velocity decreases, such as when a ball is rolling uphill.

10. 4.1 The difference between velocity and acceleration
If both velocity and acceleration are negative the speed increases but the motion is still in the negative direction.
Suppose a ball is rolling down a ramp sloped downhill to the left.
Motion to the left is defined to be negative so the velocity and acceleration are both negative.
The velocity of the ball gets LARGER in the negative direction, which means the ball moves faster to the left.

11. 4.1 Calculating acceleration
Acceleration is the change in velocity divided by the change in time. The Greek letter delta (Δ) means “the change in.”
Change in speed (m/sec)
Acceleration
(m/sec2)
a = Dv Dt
Change in time (sec)

12. 4.1 Calculating acceleration
The formula for acceleration can also be written in a form that is convenient for experiments.

13. Calculating acceleration in m/s2
A student conducts an acceleration experiment by coasting a bicycle down a steep hill. A partner records the speed of the bicycle every second for five seconds. Calculate the acceleration of the bicycle.
You are asked for acceleration.
You are given times and speeds from an experiment.
Use the relationship a = (v2 – v1) ÷ (t2 – t1)
Choose any two pairs of time and speed data since the change in speed is constant.
a = (6 m/s 4 m/s) ÷ (3 s – 4 s) = (2 m/s) ÷ (-1 s)
a = −2 m/s

14. 4.1 Constant speed and constant acceleration
Constant acceleration is different from constant speed.
If an object is traveling at constant speed in one direction, its acceleration is zero.
Motion with zero acceleration appears as a straight horizontal line on a speed versus time graph.

15. 4.1 Uniform acceleration
Constant acceleration is sometimes called uniform acceleration.
A ball rolling down a straight ramp has constant acceleration because its speed is increasing at the same rate.
Falling objects also undergo uniform acceleration.

16. 4.1 Constant negative acceleration
Consider a ball rolling up a ramp.
As the ball slows down, eventually its speed becomes zero and at that moment the ball is at rest.
However, the ball is still accelerating because its velocity continues to change.

17. 4.1 The speed vs. time graph for accelerated motion
In this experiment, velocity and acceleration are in the same direction.
No negative quantities appear, and the analysis simply uses speed instead of velocity.

19. 4.1 Slope and Acceleration
Use slope to recognize acceleration on 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).

20. Calculating acceleration
The graph shows the speed of a bicyclist going over a hill. Calculate the maximum acceleration of the cyclist and calculate when in the trip it occurred.
You are asked for maximum acceleration.
You are given a graph of speeds vs. time.
Use the relationship a = slope of graph
The steepest slope is between 60 and 70 seconds, when the speed goes from 2 to 9 m/s.
a = (9 m/s – 2 m/s) ÷ (10 s)
a = 0.7 m/s2