Four different objects are placed on a number line at 0. The chart describes the motion of each object.
| Object | Motion |
|---|---|
| $W$ | 3 units left, then 3 units right |
| $X$ | 6 units right, then 18 units right |
| $Y$ | 8 units left, then 24 units right |
| $Z$ | 16 units right, then 8 units left |
Using the information in the chart, the distance and displacement of each object can be determined. Which object has a distance that is three times as great as its displacement?
A. W
B. X
C. Y
D. Z
Answer (1)
Object W: Distance = 6, Displacement = 0.
Object X: Distance = 24, Displacement = 24.
Object Y: Distance = 32, Displacement = 16.
Object Z: Distance = 24, Displacement = 8. The distance of object Z is three times its displacement, so the answer is Z .
Explanation
Analyzing the Problem Let's analyze the motion of each object to determine the distance it traveled and its final displacement from the starting point.
Object W For object W:
It moves 3 units to the left, then 3 units to the right.
Distance traveled: 3 + 3 = 6 units.
Displacement: − 3 + 3 = 0 units.
Object X For object X:
It moves 6 units to the right, then 18 units to the right.
Distance traveled: 6 + 18 = 24 units.
Displacement: 6 + 18 = 24 units.
Object Y For object Y:
It moves 8 units to the left, then 24 units to the right.
Distance traveled: 8 + 24 = 32 units.
Displacement: − 8 + 24 = 16 units.
Object Z For object Z:
It moves 16 units to the right, then 8 units to the left.
Distance traveled: 16 + 8 = 24 units.
Displacement: 16 − 8 = 8 units.
Comparing Distance and Displacement Now, we need to find the object for which the distance traveled is three times its displacement.
For object W: The displacement is 0, so the ratio is undefined.
For object X: The ratio of distance to displacement is 24 24 = 1 .
For object Y: The ratio of distance to displacement is 16 32 = 2 .
For object Z: The ratio of distance to displacement is 8 24 = 3 .
Final Answer Therefore, object Z has a distance that is three times its displacement.
Examples
Understanding displacement and distance is crucial in physics and everyday life. For example, imagine you are tracking a delivery truck. The distance the truck travels tells you about fuel consumption and wear on the vehicle. The displacement, however, tells you how far the delivery point is from the starting location, which is important for logistics and planning efficient routes. By analyzing both distance and displacement, you can optimize delivery schedules and reduce costs.
