Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
austin takes 1 minute and 45 seconds to run three - quarters of a circular track. his rate of motion is (pi/square) radians per second.

Explanation:

Step1: Convert time to seconds

1 minute = 60 seconds, so 1 minute and 45 seconds = 60 + 45 = 105 seconds.

Step2: Find the angle covered

Three - quarters of a circular track. A full circle is \(2\pi\) radians, so three - quarters of a circle is \(\frac{3}{4}\times2\pi=\frac{3\pi}{2}\) radians.

Step3: Calculate the angular speed

Angular speed \(\omega=\frac{\theta}{t}\), where \(\theta\) is the angle and \(t\) is the time. Here, \(\theta = \frac{3\pi}{2}\) radians and \(t = 105\) seconds. So \(\omega=\frac{\frac{3\pi}{2}}{105}=\frac{3\pi}{2\times105}=\frac{\pi}{70}\) radians per second. So the denominator is 70.

Answer:

70