Question

A car initially traveling at 32.4 m/s undergoes a constant negative acceleration of magnitude 1.70 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?

Answer 1

The car tire makes 149 revolutions before coming to stop.

Explanation:

a) We have equation of motion v² = u² + 2as

Initial velocity, u = 32.4 m/s  

Acceleration, a = -1.70 m/s²  

Final velocity, v = 0 m/s  

Substituting  

v² = u² + 2as

0² = 32.4² + 2 x -1.70 x s

s = 308.75 m  

Distance traveled before stopping is 308.75 m

Radius of tire = 0.330 m

Circumference of tire = 2πx 0.33 = 2.07 m

1 revolution = 2.07 m

$\texttt{Number of revolutions = }\frac{308.75}{2.07}=148.91$

The car tire makes 149 revolutions before coming to stop.