Question

Figure shows the variation of force acting on a body with time. Assuming the body to start from rest, the variation of its momentum with time is best represented by which plot?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

From $0$ to $2$ s: at any time $t,F=10t$
$\Rightarrow a=F/m=10t/m$
$\Rightarrow {\int }_0^{v}dv={\int }_0^t\frac{10t}{m}dt\Rightarrow v=\frac{5t^2}{m}$
Momentum: $p=mv=5t^2$
$Att=2s,p=5{\left(2\right)}^2=20kgm{s}^{-1},v=20m$
from $2to4s:F=40-10t$
${\int }_{20/m}^{v}dv={\int }_2^t\frac{40-10t}{m}dt\Rightarrow v=\frac{1}{m}\left[40t-40-5t^2\right]$
$P=mv=40t-40-5t^2$