Chapter 6.1, Problem 26E

To determine

To determine (a) which car is ahead after one minute (b) what is the meaning of the area of the shaded region (c) Which car is ahead after two minutes? (d) Estimate the time at which the cars are again side by side for the given figure.

  

Answer to Problem 26E

1. Car $A$ is ahead after one minute.
2. The area of the shaded region means the distance between two cars $A$ and $B$ after one minute.
3. Car $A$ is ahead after two minutes
4. After two minutes, the area under the graph of $A$ and that of $B$ are same. Therefore, the moving distance of $A$ and $B$ during first two minutes are same and the cars are side by side.

Explanation of Solution

Given information: Consider the figure

  

Calculation:

1. Car $A$ is ahead after one minute, because the area under the graph, which is the moving distance is larger.
2. The area of the shaded region means the distance between two cars $A$ and $B$ after one minute.
3. Car $A$ is ahead after two minutes
4. After two minutes, the area under the graph of $A$ and that of $B$ are same. Therefore, the moving distance of $A$ and $B$ during first two minutes are same and the cars are side by side.