Answer to Essential Question 2.2: I

Answer to Essential Question 2.2: If we take the average of the two velocities we found in Example 2.2B, and , we get . This is clearly not the
average velocity, because we found the average velocity to be +0.80 m/s in Example 2.2A . The reason the average velocity differs from the average of the velocities of the two parts of the motion is that one part of the motion takes place over a longer time interval than the other (4 times longer, in this case). If we wanted to find the average velocity by averaging the velocity of the different parts, we could do a weighted average, weighting the velocity of the first part of the motion four times more heavily because it takes four times as long, as follows:
.
2-3 Different Representations of Motion
There are several ways to describe the motion of an object, such as explaining it in words, or using equations to describe the motion mathematically. Different representations give us different perspectives on how an object moves. In this section, we’ll focus on two other ways of representing motion, drawing motion diagrams and drawing graphs. We’ll do this for motion with constant velocity - motion in a constant direction at a constant speed.
EXPLORATION 2.3A – Learning about motion diagrams
A motion diagram is a diagram in which the position of an object is shown at regular time intervals as the object moves. It’s like taking a video and over-laying the frames of the video.
Step 1 - Sketch a motion diagram for an object that is moving at a constant velocity. An object with constant velocity travels the same distance in the same direction in each time interval. The motion diagram in Figure 2.9 shows equally spaced images along a straight line. The numbers correspond to times, so this object is moving to the right with a constant velocity.
Figure 2.9: Motion diagram for an object that has a constant velocity to the right.
Step 2 - Draw a second motion diagram next to the first, this time for an object that is moving parallel
to the first object but with a larger velocity. To be consistent, we should record the positions of the two objects at the same times. Because the second object
is moving at constant velocity, the various images of the second object on the motion diagram will also be equally spaced. Because the second object is moving faster than the first, however, there will be more space between the images of the second object on the motion diagram – the second object covers a greater distance in the same time interval. The two motion diagrams are shown in Figure 2.10.
Figure 2.10: Two motion diagrams side by side. These two motion diagrams show objects with a constant velocity to the right but the lower object (marked by the square) has a higher speed, and it passes the one marked by the circles at time-step 3.
Key ideas: A motion diagram can tell us whether or not an object is moving at constant velocity. The farther apart the images, the higher the speed. Comparing two motion diagrams can tell us which object is moving fastest and when one object passes another.
Related End-of-Chapter Exercises: 23 and 24
Chapter 2 – Motion in One Dimension
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