Question

A car moving along a circular path of radius $R$ with uniform speed covers an angle $\theta$

during a given time $t$. What is its average velocity?

• A. $\frac{2Rsin\left(\theta /2\right)}{t}$
  
• B. $\frac{2Rcos\left(\theta /2\right)}{t}$
• C. $\frac{2Rsin\left(\theta \right)}{t}$
• D. $\frac{Rsin\left(\theta /2\right)}{t}$

Answer 1

The correct option is A. $\frac{2Rsin\left(\theta /2\right)}{t}$.

If it covers angle $\theta$, then separation between initial and final point is the length of chord for any angle $\theta$ in a circle given by $2Rsin\frac{\theta }{2}$.

Average velocity is given by total displacement divided by total time taken.

So $V_{av}$=$\frac{2Rsin\frac{\theta }{2}}{t}$

So best possible answer is option A.