   Chapter 7, Problem 11P

Chapter
Section
Textbook Problem

A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2 after its brakes are applied, (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330 m? (b) What is the angular speed of the wheels when the car has traveled half the total distance?

a)

To determine
The number of revolution the car tires have made before coming to rest.

Explanation

Given info: The initial velocity of the car is 29.0ms-1 . The constant negative acceleration as the brakes are applied has a magnitude of 1.75ms-2 . The radius of the tires is 0.330m .

Explanation:

From equation of motion,

vf2=v02+2aΔx

• vf is the final velocity
• v0 is the initial velocity
• a is the acceleration
• Δx is the linear displacement

The linear displacement is given by,

Δx=vf2v022a       (1)

The linear distance covered by the car in one full revolution of the car is,

Δx1=2πr

• r is the radius of the tires

Since the car does not skid, the entire linear distance covered by the tire will correspond to rotation of the car

b)

To determine
The angular speed of the wheels when the car has travelled half the total distance.

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