   Chapter 2, Problem 12CQ

Chapter
Section
Textbook Problem

A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance vt. (b) The average speed of the car is v/2. (c) The acceleration of the car is v/t. (d) The velocity of the car remains constant. (e) None of these.

To determine
The distance, velocity, and the acceleration of a car.

Explanation

The car starts from its rest.

The constant acceleration is,

a=vut

Here,

v is the final velocity.

u is the initial velocity.

a is the acceleration.

t is the time.

Substitute 0 for u to find a .

a=v0t=vt

The average velocity of the car is,

v¯=vu2

Here,

v¯ is the average velocity

Substitute 0 for u to find v¯ .

v¯=v02=v2

The displacement of the car is,

s=v¯t

Here,

s is displacement of the car.

Substitute v/2 for v¯ to find s

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