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

Options

A.
B.
C.
D.

Answer

C

Explanation

From 0 to 2 s: at any time t, `F=10t`
`implies a=F//m=10t//m`
`implies int_(0)^(v)dv=int_(0)^(v) (10t)/(m)dt implies v=(5t^(2))/(m)`
Momentum : `P=mv=5t^(2)`
At `t=2s , P=5(2)^(2)=20 kgms^(-1), v=20//m`
from 2 to 4 s: `F=40-10 t`
`int_(20//m)^(v) dv = int_(2)^(t) (40-10t)/(m)dt implies v=1/(m) [40t-40-5t^(2)]`
`P=mv=40t-40-5t^(2)`.