Question

A particle of mass $0.1 kg$ 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 $x = 12\, m$ is

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

Answer 1

Answer: (D)

Area between curve and displacement axis
$= \frac{1}{2} \times\left(12 +4\right) \times10 = 80J$
In this time, body acquires kinetic energy $= \frac{1}{2}mv^{2}$
By the law of conservation of energy $\frac{1}{2}mv^{2} = 80 J$
$\Rightarrow \frac{1}{2} \times0.1 \times v^{2} =80$
$\Rightarrow v^{2} = 1600$
$\Rightarrow v = 40 m/s$