Question

The acceleration-displacement graph of particle moving in a straight line is as shown in figure, initial velocity of particle is zero. Find the velocity of the particle when displacement of the particle is $s=12m$.

• A. $4\sqrt{3}m{s}^{-1}$
• B. $4\sqrt{2}m{s}^{-1}$
• C. $2\sqrt{3}m{s}^{-1}$
• D. $2\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is A $4\sqrt{3}m{s}^{-1}$

$a=v\frac{dv}{dx}\Rightarrow adx=vdv\Rightarrow {\int }_0^{12}adx={\int }_0^{V}vdv\Rightarrow Areaunderthecurve=\frac{V^2}{2}\Rightarrow \frac{V^2}{2}=24\Rightarrow V=4\sqrt{3}$