Question

A stationary particle of mass $m=1.5kg$ is acted upon by a variable force. The variation of force with respect to displacement is plotted in fig.
What is the maximum speed attained by the particle and at what time is it attained?

Answer 1

Velocity attained will be maximum at $x=x_0$. become after this work done is negative or force is opposite to velocity
$W=\frac{1}{2}\times \frac{10}{3}\times 100=\frac{500}{3}J$
$\Rightarrow \frac{1}{2}m{v}^2=\frac{500}{3}\Rightarrow \frac{1}{2}\times \frac{15}{10}{v}^2=\frac{500}{3}$
$\Rightarrow v=\sqrt{\frac{5000\times 2}{45}}=\frac{10\sqrt{20}}{3}m{s}^{-1}=\frac{20}{3}\sqrt{5}m{s}^{-1}$