1.3.3 Motion Diagrams with Displacement Vectors

The first step in analyzing a motion diagram is to determine all of the displacement vectors, which are simply the arrows connecting each dot to the next. Label each arrow with a vector symbol Δr⃗n, starting with n=0. FIGURE 1.7 shows the motion diagrams of Figure 1.4 redrawn to include the displacement vectors.

FIGURE 1.7 Motion diagrams with the displacement vectors.

The figure consists of two parts labeled ('a") and (b) that illustrate the motion diagram of a rocket launch and a stopping car.
FIGURE 1.7 Full Alternative Text

NOTE   When an object either starts from rest or ends at rest, the initial or final dots are as close together as you can draw the displacement vector arrow connecting them. In addition, just to be clear, you should write “Start” or “Stop” beside the initial or final dot. It is important to distinguish stopping from merely slowing down.

Now we can conclude, more precisely than before, that, as time proceeds:

EXAMPLE 1.1 Headfirst into the snow

Alice is sliding along a smooth, icy road on her sled when she suddenly runs headfirst into a large, very soft snowbank that gradually brings her to a halt. Draw a motion diagram for Alice. Show and label all displacement vectors.

MODEL The details of Alice and the sled—their size, shape, color, and so on—are not relevant to understanding their overall motion. So we can model Alice and the sled as one particle.

VISUALIZE FIGURE 1.8 shows a motion diagram. The problem statement suggests that the sled’s speed is very nearly constant until it hits the snowbank. Thus the displacement vectors are of equal length as Alice slides along the icy road. She begins slowing when she hits the snowbank, so the displacement vectors then get shorter until the sled stops. We’re told that her stop is gradual, so we want the vector lengths to get shorter gradually rather than suddenly.

FIGURE 1.8 The motion diagram of Alice and the sled.

The figure illustrates the motion diagram of a sled coming to a stop.