Question

Figure shows the force (F) versus displacement (s) graph for a particle of mass m=2 kg initially at rest
(i) The maximum, speed of the particle occurs at x = _______.
(ii) The maximum speed of the particle is _________.

Answer 1

(i) the maximum speed of particle occurs when force is Zero.

$\therefore$ at $x=3$

(ii) $\int Fdx=\frac{1}{2}m{v}^2$

$\begin{array}{c}\Rightarrow \frac{1}{2}\left(5+10\right)1+\frac{1}{2}\times 2\times 10=\frac{1}{2}\times 2\times v^2\\ \Rightarrow \frac{15}{2}+10=v^2\\ \Rightarrow v^2=\frac{25}{2}\\ \Rightarrow v=\sqrt{\frac{25}{2}}m/s\end{array}$.