Question

A body of mass 4 kg is moving with momentum of $8\, kg\, m\, s^{-1}$. A force of 0.2 N acts on it in the direction of motion of the body for 10 seconds. The increase in kinetic energy in joules is

• A. $10$
• B. $8.5$
• C. $4.5$
• D. $4$

Answer 1

Answer: (C)

Momentum = mass × velocity
$p = mu$
$u=\frac{p}{m}=\frac{8\,kg\,m\,s^{-1}}{4\,kg}=2\,m\,s^{-1}$
$Acceleratio=\frac{Force}{Mass}$
$a=\frac{0.2\,N}{4\,kg}=0.05\,m\,s^{-2}$
Distance travelled by the body in $10\, s$ is
$S=ut+\frac{1}{2}at^{2}$
$=\left(2\,m\,s^{-1}\right)\left(10\,s\right)+\frac{1}{2}\times\left(0.05\,m\,s^{-2}\right)\left(10\,s\right)^{2}$
$=20\,m+2.5\,m=22.5\,m$
Work done, $W = FS$
$= \left(0.2\,N\right)\left(22.5\,m\right)=4.5\,J$
According to work-energy theorem
Increase in kinetic energy = Work done
$=4.5\,J$