Question

The acceleration of a body starting from rest is given by $a=13-0.1s$, where $a$ is the acceleration (in $m/s^2$) and $s$ is the displacement (in $m$). If its mass is $2kg$, find its momentum when the displacement is $100m$.

• A. $40Ns$
• B. $80Ns$
• C. $120Ns$
• D. $130Ns$

Answer 1

The correct option is B $80Ns$

$a=\frac{dv}{dt}=v\frac{dv}{ds}$
$\Rightarrow {\int }_0^{v}vdv={\int }_0^{100}(13-0.1s)ds$
$\Rightarrow \frac{v^2}{2}{|}_0^v=(13s-\frac{0.1s^2}{2}){|}_0^{100}$
$\Rightarrow \frac{v^2}{2}=(1300-500)$
$\Rightarrow v=40m/s$
Hence, Momentum $p=2\times 40=80Ns$