Question

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

• A. $0m/s$
• B. $20\sqrt{2}m/s$
• C. $30\sqrt{3}m/s$
• D. $40m/s$

Answer 1

Answer: (D)

Area between curve and displacement axis
$=\frac{1}{2}\times \left(12+4\right)\times 10=80J$
In this time, body acquires kinetic energy $=\frac{1}{2}m{v}^2$
By the law of conservation of energy $\frac{1}{2}m{v}^2=80J$
$\Rightarrow \frac{1}{2}\times 0.1\times v^2=80$
$\Rightarrow v^2=1600$
$\Rightarrow v=40m/s$