Question

The 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 $S_o=20m.$ At what displacement do velocity and acceleration have the same magnitudes?

• A. $\text{At}S=5m$
• B. $\text{At}S=10m$
• C. $\text{At}S=30m$
• D. None of these

Answer 1

The correct option is D None of these


For $S=0$ to $S=S_o$
$V=\frac{V_{o}S}{S_o}\text{and a}=\frac{V_o^2}{S_o^2}S$
If velocity and acceleration have same magnitudes,
$V=a\Rightarrow V_o=S_o$ which is not possible with the given values of $V_o$ and $S_o$.
For $S=S_o$ to $S=2S_o$
$V=\frac{-V_o}{S_o}S+2V_o=-\frac{4}{20}S+2V_o$
$=-\frac{S}{5}+8$
$a=\frac{V_o^2}{S_o^2}.S-\frac{2V_o^2}{S_o}={\left(\frac{4}{20}\right)}^2.S-\frac{2\times 4^2}{40}$
$=\frac{S}{25}-\frac{8}{5}$
$\text{If velocity and acceleration have same magnitudes},$
$V=a\Rightarrow -\frac{S}{5}+8=\frac{S}{25}-\frac{8}{5}$
$\Rightarrow S=40m$