Question

A particle of mass 0.1 kg is subjected to a force, which varies with the 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 ms${}^{-1}$
• B. 20$\sqrt{2}$ ms${}^{-1}$
• C. 20$\sqrt{3}$ ms${}^{-1}$
• D. 40 ms${}^{-1}$

Answer 1

Answer: (D)

40 ms${}^{-1}$

Work done by particle under application of an external force=$\int Fdx$

=Area under the $F$ vs $x$ curve=$\frac{1}{2}\times (4+12)\times 10J$

$=80J$

This work done goes into the kinetic energy of the particle

Thus $\frac{1}{2}m{v}^2=80$

$⟹\frac{1}{2}\times 0.1\times v^2=80$

$⟹v=40m/s$