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 $t, F =10 t$
$\Rightarrow a= F/m=10 t/m$
$\Rightarrow \int_{0}^{v}dv =\int_{0}^{t} \frac{10t}{m} dt \Rightarrow v=\frac{5t^{2}}{m}$
Momentum: $p = mv =5t^{2}$
$At t = 2s, p =5\left(2\right)^{2} = 20 \,kg \,ms^{-1}, v = 20 m$
from $2to 4 s: F=40 -10 t$
$\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}$