Question

A particle moves according to the law $x=r\cos \frac{\pi t}{2}$. The distance covered by it in the time interval between $t=0$ and $t=3s$ is

• A. $r$
• B. $2r$
• C. $3r$
• D. $4r$

Answer 1

Answer: (C)

$3r$

Position of particle $x=r\cos \frac{\pi t}{2}$

At $t=0s$, $x=r\cos 0=r$

So, at $t=0s$, particle is at extreme position of SHM.

Time period of oscillation $T=\frac{2\pi }{w}=\frac{2\pi }{\pi /2}=4s$

In one time period, distance moved by particle $=4r$

So, in $3s$ distance moved $=\frac{3}{4}\times 4r=3r$