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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4, Problem 19P

To determine

That at some time during the race, the acceleration of both the cars are same.

Expert Solution

**Given information:**

In an automobile race along a straight road, car A passes car B twice.

**Calculations:**

Let

Let

Now it is given that A passes B twice, therefore there exist (at least) three times when their positions are equal.

Let,

Now position of the cars at time

By the mean value theorem, there exists a time

Applying the mean value theorem again, this time to the function

Now,

so

Thus we can see that the acceleration of both the cars are same at some time