A particle moves over three quarters of a circle of radius $r$ in time $t$. Find the speed of the particle.

As given, a particle moves over three quarters of a circle of radius $r$.

The motion of the particle has been shown in the diagram below:


Distance travelled $\frac{3}{4}$of the circumference of the circle

$=\frac{3}{4}\times2\pi r$

$=\frac{3}{2}\pi r$

Therefore, speed$=\frac{distance}{time}$$

$=\frac{\frac{3}{2}\pi r}{t}$

$=\frac{3}{2t}\pi r$

Updated on: 10-Oct-2022

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