Question

A cyclist is riding such that the wheels of the bicycle have a rotation rate of 3.0 rev/s. If the cyclist brakes such that the rotation rate of the wheels decrease at a rate of 0.3 rev/s², how long does it take for the cyclist to come to a complete stop?

a) 10 s
b) 20 s
c) 30 s
d) 40 s

Answer 1

To find the time it takes for the cyclist to come to a complete stop, use the formula ω_f = ω_i + αt, where ω_f is the final angular velocity, ω_i is the initial angular velocity, α is the angular acceleration, and t is the time taken. In this case, t is 10 seconds.

Step-by-step explanation:

To find the time it takes for the cyclist to come to a complete stop, we can use the formula:

ω_f = ω_i + αt

Where ω_f is the final angular velocity, ω_i is the initial angular velocity, α is the angular acceleration, and t is the time taken.

In this case, the initial angular velocity is 3.0 rev/s, the angular acceleration is -0.3 rev/s², and we want to find the time it takes for the cyclist to stop, so the final angular velocity would be 0 rev/s.

Plugging in the values into the formula, we have:

0 = 3.0 - 0.3t

Solving for t, we get:

t = 10 s

Therefore, it will take the cyclist 10 seconds to come to a complete stop.