Question

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

• A. $2a$
• B. $3a$
• C. $4a$
• D. $5a$

Answer 1

The correct option is B $3a$

Given,

$X=acos\left(\frac{\pi }{2}t\right)$

$X{|}_{t=0s}=acos(\frac{\pi }{2}\times 0)=a$

$X{|}_{t=3s}=acos\left(\frac{3\pi }{2}\right)=0$

Phase, $\Delta \varphi =\varphi {|}_{t=3s}-\varphi {|}_{t=0}$

$\Delta \varphi =\frac{3\pi }{2}-0=\frac{3\pi }{2}$

The total distance distance covered is $S=a+a+a$

$S=3a$

The correct option is B.