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. $10\text{m/s}$
• B. $20\text{m/s}$
• C. $20\sqrt{3}\text{m/s}$
• D. $40\text{m/s}$

Answer 1

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

According to Work Energy theorem :
Total work done = Area under $(F-x)$ curve $=\Delta K.E.$
$\Rightarrow \frac{1}{2}\left(4\right)\left(10\right)+\frac{1}{2}\left(4\right)10+4\times 10=\Delta K.E.$
As particle is starting from rest, $\Delta KE=\frac{1}{2}m{v}^2$
$\Rightarrow 80\text{J}=\frac{1}{2}\left(0.1\right)v^2\Rightarrow v=40\text{m/s}$