Question

A race car on a 150-metre-long track has a uniform acceleration from 10 m/s to 20 m/s travelling the full distance of the track. Each wheel of the car has a 250-millimetre radius. Which statement must be true?

A. The time the car is accelerating is 5 seconds.
B. The linear acceleration of a point on each of the wheels is
4 (m/s)^2.
C. The angular acceleration of each of the wheels is 4 (rad/s)^2.
D. The initial angular velocity of each of the wheels is 20 rad/s.

Answer 1

The correct statement is C. The angular acceleration of each of the wheels is 4 (rad/s)^2.

The car has a uniform acceleration from 10 m/s to 20 m/s, so the average speed is (10 m/s + 20 m/s) / 2 = 15 m/s. The time it takes to travel the 150-metre-long track at this average speed can be found using the equation:

distance = speed x time

time = distance / speed = 150 m / 15 m/s = 10 s

The linear acceleration of a point on each wheel can be found using the equation:

a = (vf - vi) / t = (20 m/s - 10 m/s) / 10 s = 1 m/s^2

The angular acceleration of each wheel can be found using the equation:

alpha = a / r = 1 m/s^2 / 0.25 m = 4 rad/s^2

The initial angular velocity of each wheel is not given in the problem, so statement D is not necessarily true.