Question

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

• A. 7
• B. 8
• C. 9
• D. 4

Answer 1

The correct option is D

4

$v=\frac{ds}{dt}=4\sqrt{1+s}\Rightarrow {\int }_o^s\frac{ds}{\sqrt{1+s}}=4{\int }_o^{t}dt\Rightarrow 4t=2[\sqrt{1+s}-1]\Rightarrow 2t+1=\sqrt{1+s}\Rightarrow 1+s=4t^2+1+4t\Rightarrow s=4t^2+4tAtt=0s,s=0m\Rightarrow v{|}_{att=0s}=4\sqrt{1+0}=4m{s}^{-1}$