Q. A particle of a mass $0.1\ kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\ m$ is
A) $0\ m/s$
B) $20\sqrt{2}\ m/s$
C) $20\sqrt{3}\ m/s$
D) $40\ m/s$
Explanation
(d) Area between curve and displacement axis
$= \frac{1}{2} \times (12 + 4) \times 10 = 80\ J$
In this time body acquire kinetic energy $= \frac{1}{2}\ mv^{2}$
By the law of conservation of energy
$\frac{1}{2}mv^{2} = 80\ J$
$\Rightarrow \frac{1}{2}\ \times 0.1 \times v^{2} = 80 \Rightarrow v^{2} = 1600 \Rightarrow v = 40\ m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.