Question

A particle moving in a straight line has velocity-displacement equation as $v=5\sqrt{1+s}.$ Here $v$ is in $m{s}^{-1}$ and $s$ in meter. Select the correct alternative.

• A. Particle is initially at rest
• B. Initially velocity of the particle is $5$ m/s and the particle has a constant acceleration of $12.5$ $m{s}^{-2}$
• C. particle moves with a uniform velocity
• D. None of the above

Answer 1

Answer: (B)

Initially velocity of the particle is $5$ m/s and the particle has a constant acceleration of $12.5$ $m{s}^{-2}$

Comparing the given equation with the kinematic equation $v^2=u^2+2as$ we get $u_{initial}=5m/s$
$a=5\left(\frac{1}{2\sqrt{1+s}}\right)(0+ds/dt)=\frac{5v}{2\sqrt{1+s}}=\frac{5\times 5\sqrt{1+s}}{2\sqrt{1+s}}=25/2=12.5m/s$