Question

A particle moving in straight line diverse a distance $x$ in that straight line from a fixed point in time $t$. If $x=a\cos \sqrt{\mu }t$ {Where $\mu >0$). Find the acceleration of the particle in time $t$.

• A. $-\mu x$
• B. $\mu x$
• C. $-\sqrt{\mu }x$
• D. $\sqrt{\mu }x$

Answer 1

Answer: (A)

$-\mu x$

The displacement of the particle in time $t$ is given by

$x=a\cos \sqrt{\mu }t$

The acceleration of the particle in time $t$ is given by $\frac{d^{2}x}{d{t}^2}$.

Now, $\frac{dx}{dt}=-a\sqrt{\mu }\sin \sqrt{\mu }t$

And

$\frac{d^{2}x}{d{t}^2}=-a(\sqrt{\mu }{)}^2\cos \sqrt{\mu }t=-\mu x$.