   Chapter 5, Problem 20CQ

Chapter
Section
Textbook Problem

A car accelerates uniformly from rest. Ignoring air friction, when does the car require the greatest power? (a) When the car first accelerates from rest,  (b) just as the car reaches its maximum speed, (c) when the car reaches half its maximum speed. (d) The question is misleading because the power required is constant. (e) More information is needed.

To determine
When does the car require more power.

Explanation

Given Info:

The car is accelerating uniformly from rest.

Since, the car is accelerating from rest with a uniform acceleration; the net force acting on the car will be a constant.

Thus,

Formula to calculate the instantaneous power given to the car is,

P=Fv

• F is the constant net force acting on the car
• v is the speed of the car

Since, the powered required for the car is directly proportional to the speed of the car and the force given to the car is a constant; the car requires more power when it reaches its maximum speed.

Conclusion:

Since, the car is moving in a uniform acceleration and the required power is directly proportional to the speed of the car, the car requires more power when it reaches its maximum power

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