Question

A particle of mass $0.1\text{kg}$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12\text{m}$ is

• A. $0\text{m/s}$
• B. $20\sqrt{2}\text{m/s}$
• C. $20\sqrt{3}\text{m/s}$
• D. $40\text{m/s}$

Answer 1

The correct option is D $40\text{m/s}$

Total work done = Area under $F-x$ curve
$=\Delta K.E$
$\Rightarrow \frac{1}{2}\left(4\right)\left(10\right)+\frac{1}{2}\left(4\right)10+40=\Delta KE$
$\Rightarrow 80=\frac{1}{2}\left(0.1\right)v^2$
(since initial velocity is zero)
$\Rightarrow v=40\text{m/s}$