# The runners run the race and the compare the run race. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.6, Problem 12E

(a)

To determine

## To describe: The runners run the race and the compare the run race.

Expert Solution

### Explanation of Solution

Given:

The position functions of two runners A and B who run a 100-meter race and finish in a tie.

Calculation:

Form given Figure, it is observed that the graph of A is a line.

Note that, the slope of the line is same as all points.

The slope of the line is constant at entire 100 meter race.

Note that, the slope of the tangent to the curve at a means that the derivative of the curve at a.

The derivative of A’s path is constant.

That is, runner A finished 100 meter race with constant velocity.

From given Figure, it is observed that the slope of the graph of B.

The slope of tangent to the graph B is increasing when time is increase.

That is, the value of derivative of the graph B is increasing when the time increase.

Thus, the velocity of the runner B is increasing.

The slope of the graph B is less than the slope of the graph A when start the race and The slope of the graph B is more than the slope of the graph A when end the race.

That is, the velocity of runner B is less than the velocity of runner A when start the race and the velocity of runner B is more than the velocity of runner A when end the race.

(b)

To determine

Expert Solution

### Explanation of Solution

From the graph, it is observed that the vertical line between the graph A and graph B is length when the time is 9 and 10 seconds.

The time 9 and 10 seconds when the distance between the runners the greatest.

(c)

To determine

### To find: The time when they have same velocity.

Expert Solution

The time 9.5 seconds when they have same velocity.

### Explanation of Solution

From Figure 1, Compare the slope of the curve A and slope of the curve B at each point.

The slope of the curve A and slope of the curve B is same when time 9.5 seconds.

That is, the derivative value same of both curves when time when time 9.5 seconds.

Therefore, the time 9.5 seconds when they have same velocity.

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