Question

A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?

a) 0.007 rad/s
b) 0.014 rad/s
c) 0.021 rad/s
d) 0.028 rad/s

Answer 1

The track star's angular velocity on a 400-m circular track, with an assumption of constant speed and completion time of 45 seconds, is approximately 0.014 rad/s (choice d).

Step-by-step explanation:

The student's question involves calculating angular velocity in the context of a track star running a 400-m race on a circular track. To find the angular velocity, we use the formula ω = Θ/t, where ω is the angular velocity in radians per second, Θ is the angle in radians, and t is the time in seconds. In one complete lap on a circular track, the track star covers an angle of 2π radians (equivalent to 360 degrees). Given that the track star completes the lap in 45 seconds, the angular velocity can be calculated as follows:

ω = Θ/t = 2π rad / 45 s = 0.1396 rad/s

Therefore, the closest answer from the provided choices would be (d) 0.014 rad/s, when the angular velocity is rounded to three significant figures.