Question

Velocity $\left(V\right)$ versus displacement $\left(S\right)$ graph of a particle moving in a straight line is as shown in the figure. Given $V_o=4m/s$ and $S_o=20m.$
Corresponding acceleration $\left(a\right)$ versus displacement $\left(S\right)$ graph of the particle would be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

From $S=0$ to $S=S_o$ velocity is given by,
$V=\frac{V_o}{S_o}S\Rightarrow \frac{dV}{dt}=\frac{V_o}{S_o}\left(\frac{dS}{dt}\right)$
$\Rightarrow \text{Acceleration,}a=\frac{V_o}{S_o}\left(\frac{V_o}{S_o}S\right)$
$\Rightarrow a=\frac{V_o^2}{S_o^2}.S$
$\Rightarrow a\propto S$
From $S=S_o\text{to}S=2S_o,$ velocity is given by
$V=\frac{-V_o}{S_o}S+2V_o$
$\frac{dV}{dt}=\frac{-V_o}{S_o}\left(\frac{dS}{dt}\right)$
$\text{Accleration,}a=\frac{-V_o}{S_o}(\frac{-V_o}{S_o}S+2V_o)=\frac{V_o^2}{S_o^2}.S-\frac{2V_o^2}{S_o}$
$\text{At}S=S_o,a=\frac{-V_o^2}{S_o}\text{and at}S=2S_o,a=0$
Hence, graph (a) is correct.