1. Motion Along a Straight Line
Chapter 2
Motion Along a Straight Line

2. Goals for Chapter 2 To study motion along a straight line
To define and differentiate average and instantaneous linear velocity
To define and differentiate average and instantaneous linear acceleration
To explore applications of straight-line motion with constant acceleration
To examine freely falling bodies
To consider straight-line motion with varying acceleration

3. Introduction
Runners accelerate out of starting blocks, run faster, then slow down as the race ends.
A tree drops in front of my car. Can I stop in time?
This study of motion … kinematics … is common to our lives yet full of interesting features.

4. Displacement, time, and the average velocity—Figure 2.1
The change in position, the passing of time, and the average speed all depend on the physical situation.
Figure 2.1 allows us to illustrate each parameter.

5. The truck, its motion, and a graph—Figures 2.2 and 2.3
Motion may be analyzed graphically to understand the changes that are occurring and the data that can be extracted.

6. Average and instantaneous velocities—Figure 2.4
The speedometer on a car illustrates this point well. The average speed of a journey may be a law-abiding 55 mph, but there may be periods of dangerous behavior over the speed limit and complete stops at lights.
The swimmers in the figure exhibit similar behavior.

7. A safari and a chase—Figure 2.6
Refer to Example 2.1 and Figure 2.6 of a systematic solution of several bodies in motion.

8. Follow the motion of a particle—Figure 2.8
A graph of position versus time may be constructed.
The motion of the particle may be described at selected moments in time.

9. The average acceleration—Example 2.2
An example of the motion of an astronaut can be graphed and analyzed.
The data are tabulated on page 44, and the graphical analysis is shown below in Figure 2.10.

10. Average and instantaneous acceleration—Figure 2.11
Consider the motion of the dragster shown below.
Example 2.3 shows the analysis for the car in Figure 2.11 shown below.

11. Finding the acceleration—Figure 2.12
A graph of  and t may be used to find the acceleration.
Find the slope of a tangent line at any given point.

12. Motion with constant acceleration—Figures 2.15 and 2.17
Motion with constant positive acceleration results in steadily increasing velocity.

13. The equations of motion under constant acceleration
The pages leading to the top of page 51 follow the derivation of four equations of constant acceleration. They are shown at right.
Special mention is made of these four equations because they will permeate our study of kinematics (linear and circular, too).
Follow the steps in Problem-Solving Strategy 2.1 for any problem involving motion with constant acceleration.
vx = vox + axt
x = xo + voxt + 1/2axt2
vx2 = vox2 + 2ax(x  xo)
(x  xo) = {(1/2)(vox + vx)}t

14. Use the equations to study motorcycle motion
Refer to Example 2.4 and use the equations in a practical example illustrating a motorcycle and rider.

15. Study two bodies with different accelerations
Refer to Example 2.5 and use the equations in a practical example illustrating a motorcycle and its rider chasing an SUV.

16. Free fall—Figure 2.22
A strobe light begins to fire as the apple is dropped.
Notice how the space between images increases as the apple’s velocity grows.

17. Free fall II—Example 2.6
Aristotle thought that heavier bodies would fall faster. Galileo is said to have dropped two objects, one light and one heavy, from the top of the Leaning Tower of Pisa to test his assertion that all bodies fall at the same rate.
Refer to Example 2.6 for a worked example using the leaning tower.
Astronaut Dave Scott tested this himself by dropping a hammer and a feather on the moon. ( video15.html)

18. Free fall III—Figure 2.24
Refer to Example 2.7.
Notice the problem is solved in two steps.

19. Is velocity zero at the highest point?—Figure 2.25
A common misconception is explained.
Next, refer to Example 2.8 and an equation requiring a quadratic solution.

20. When acceleration is not constant—Figures 2.26 and 2.28
Even the smoothest sports car does not move with constant acceleration.
The motion may be integrated over many small time windows.

21. Analysis of motion—Figure 2.29
All components of motion under changing acceleration may be examined.
Refer to Examples 2.9 and 2.10.