Question

a cyclist completes half round of a circular track of radius 318 m in 1.8 minutes.find acceleration

Answer 1

Question 35694

We are given radius $R = 318 \, \text{m}$ and $t = 1.8 \, \text{min}$ . Since cyclist completes half round of the track in $t$ minutes, the time needed to complete the whole track is $T = 2t = 3.6 \, \text{min} = 216 \, \text{sec}$ (this is the period of motion).

Angular velocity is $\omega = \frac{2\pi}{T}$ , and velocity is $a = \omega^2 R$ . Thus, acceleration is $a = \frac{4\pi^2R}{T^2} = 0.27\frac{m}{s^2}$ .