Question

A stationary body accelerates at a rate of $1m{s}^{-2}$ for a distance of $18m$. If the body weighs $45kg$, find the final momentum of the body.

• A. $180kgm{s}^{-1}$
• B. $210kgm{s}^{-1}$
• C. $240kgm{s}^{-1}$
• D. $270kgm{s}^{-1}$

Answer 1

The correct option is D $270kgm{s}^{-1}$

Given: mass $m=45kg$, initial velocity $u=0$ (because, initially the body was at rest), displacement $s=18m$, and acceleration, $a=1m{s}^{-2}$
Let the final velocity of the car be $v$.

Using the third equation of motion:
$v^2=u^2+2as\Rightarrow v=\sqrt{2as}\left(\text{as u = 0}\right)$
$\Rightarrow v=\sqrt{2\times 1\times 18}=\sqrt{36}=6m{s}^{-1}$
Initial momentum $p_1=mu=0$
Final momentum $p_2=mv=45\times 6=270kgm{s}^{-1}$
Therefore the change in momentum $p=p_2-p_1=270-0=270kgm{s}^{-1}$.