Question

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