Question

A body of mass $0.5$ $kg$ travels in a straight line with velocity $v$ = $a{x}^{3/2}$ where $a$ = $5$ $m^{-1/2}$ $s^{-1}$. What is the work done by the net force during its displacement from $x$ = $0$ to $x$ = $2m$ ?

Answer 1

Mass of the body, $m=0.5kg$

Velocity of the body is governed by the equation, $v=a{x}^{3/2}$ and $a=5m^{-1/2}/s$

Initial velocity, $u$ (at $x=0$) $=0$

Final velocity $v$ (at $x=2m$) $=10\sqrt{2}m/s$

Work done, $W=$ Change in kinetic energy

$=\left(1/2\right)m(v^2-u^2$)

W $=50J$