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.
Calculate the velocity acquired by the particle after getting displaced through $6m$.

Answer 1

$\frac{x_0-2}{100}=\frac{4-x_0}{50}\to x_0=\frac{10}{3}m$

$Totalworkdone$w=\dfrac{1}{2}x_0 \times 100-\dfrac{1}{2}(6-x_0)50=100 J$

$\Rightarrow \frac{1}{2}m{v}^2=100$

$\Rightarrow \frac{1}{2}\times \frac{15}{10}{v}^2=100\Rightarrow v=\sqrt{\frac{2000}{15}}=\frac{20}{\sqrt{3}}m{s}^{-1}$