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Chapter 2 | Kinematics 45
Figure 2.16 Car B is slowing down.
Because the positive direction is considered to the right of the paper, Car B is also moving with a positive velocity. However, because it is slowing down while moving with a positive velocity, its acceleration is considered negative. (This can be viewed in a mathematical manner as well. If the car was originally moving with a velocity of +25 m/s, it is finishing with a speed less than that, like +5 m/s. Because the change in velocity is negative, the acceleration will be as well.)
Figure 2.17 Car C has a constant speed.
Because the positive direction is considered to the right of the paper, Car C is moving with a positive velocity. Because all arrows are of the same length, this car is not changing its speed. As a result, its change in velocity is zero, and its acceleration must be zero as well.
Figure 2.18 Car D is speeding up in the opposite direction of Cars A, B, C.
Because the car is moving opposite to the positive direction, Car D is moving with a negative velocity. Because it is speeding
up while moving in a negative direction, its acceleration is negative as well.
Figure 2.19 Car E is slowing down in the same direction as Car D and opposite of Cars A, B, C.
Because it is moving opposite to the positive direction, Car E is moving with a negative velocity as well. However, because it is slowing down while moving in a negative direction, its acceleration is actually positive. As in example B, this may be more easily understood in a mathematical sense. The car is originally moving with a large negative velocity (−25 m/s) but slows to a final velocity that is less negative (−5 m/s). This change in velocity, from −25 m/s to −5 m/s, is actually a positive change (
of 20 m/s. Because the change in velocity is positive, the acceleration must also be positive.
Making Connection - Illustrative Example
The three graphs below are labeled A, B, and C. Each one represents the position of a moving object plotted against time.