Question

A particle moves according to the equation $x=a\cos \left(\frac{\pi t}{2}\right)$. The distance covered by it in the time interval between $t=0$ and $t=3s$ is:

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

Answer 1

The correct option is A $2a$

$x=a\cos \frac{\pi t}{2}$

$v=\frac{dx}{dt}=-a\sin \frac{\pi t}{2}\times \frac{\pi }{2}$ when $\frac{\pi t}{2}=n\pi$ at t=2 s (particle will stop)

$=\frac{d^{2}x}{d{t}^2}=-\frac{a{\pi }^2}{4}\cos \pi t2$

from $t=0$ to $t=2s$

$S=$distance traveled

$=\left|a\cos \left(\frac{\pi \times 2}{2}\right)\right|=a$

$t=2s$ to $t=3s$

$S=$distance covered

$\left|a\cos \left(\frac{3\times \pi }{2}\right)-a\cos \left(\frac{\pi \times 2}{2}\right)\right|=a$

Total distance =2a