25. A car is accelerating when it is (a) traveling on a straight, flat road at 50 miles per hour. (b) traveling on a straight uphill road at 30 miles per hour. (c) going around a circular track at a steady 100 miles per hour.

(c) going around a circular track at a steady 100 miles per hour.

Explanation:

The acceleration of an object is equal to the rate of change of velocity of the object:

where

is the change in velocity of the object

is the time interval

We notice that velocity is a vector, so it has both a magnitude and a direction. This means that , the change in velocity, is either caused by a change in magnitude of velocity, or by a change in the direction.

Therefore, the acceleration is non-zero if at least one of the two is verified:

- There is a change in magnitude of the velocity

- There is a change in direction

Let's now analyze the three statements:

(a) traveling on a straight, flat road at 50 miles per hour. --> here there is no change in magnitude or direction of the velocity, so there is no acceleration.

(b) traveling on a straight uphill road at 30 miles per hour. --> here there is no change in magnitude or direction of the velocity, so there is no acceleration.

(c) going around a circular track at a steady 100 miles per hour. --> here there is no change in magnitude of the velocity, but the direction is changing (circular track), therefore there is acceleration.

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