Question

fig. 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

The correct option is C

From 0 to 2 s: at any time t, F = 10t

$\Rightarrow a=\frac{F}{m}=10\frac{t}{m}$

$\Rightarrow \underset{0}{\overset{v}{\int }}dv=\underset{0}{\overset{t}{\int }}\frac{10t}{m}dt\Rightarrow v=\frac{5t^2}{m}$

Momentum: $P=mv=5t^2$

At t = 2s, P = $5(2{)}^2$ = 20 kg m $s^{-1}$ , v = 20/m

From 2 to 4 s : F = 40 - 10t

$\underset{20/m}{\overset{v}{\int }}dv=\underset{2}{\overset{t}{\int }}\frac{40-10t}{m}dt\Rightarrow v=\frac{1}{m}[40t-40-5t^2]$

$P=mv=40t-40-5t^2$