Prove: the impulse: momentum theorem.

Explanation

Impulse: It is defined as the product of the average force and the time for which the force acts. i.e., `vecJ= vecF_(av)t`. SI unit of impulse is Ns
By Newton.s second law, we have
`vecF= (dvecp)/(dt)` or `vecFdt= dvecp` …(i)
Integrating the above equation within limits t=0, `p=p_(1)` and `t=t, p=p_(2)` , we have
`int_(0)^(1)vecF dt= int_(p_(1))^(p_(2))vecdp implies vecJ= int_(0)^(1)vecFdt= |P|_(p_(1))^(p_(2)) ` or `vecJ= int_(0)^(1)vecFdt= |p_(2)-p_(1)|`
Thus, change in momentum produced in a body in given time is equal to impulse. This is impuls momentum theorem.