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. $70N-s$
• B. $80N-s$
• C. $40N-s$
• D. $100N-s$

Answer 1

The correct option is B $80N-s$

$a=v\frac{dv}{ds}$

⇒${\int }_0^{v}vdv={\int }_0^{100}ads$
⇒${\int }_0^{v}vdv={\int }_0^{100}(13-0.1s)ds$
⇒$\frac{v^2}{2}=(1300-500)$ (Applying limits of integration, where lower limit for $s$ is $0$ and upper limit for $s$ is $100$)
$⟹v=40m/s$
Hence,
Momentum $p=m\times v$
$=2\times 40=80N-s$