Prove impulse momentum equation

Explanation

If a force `(F )` acts on a body in a very short interval of time `(Detla t)` then form Newton's second law in magnitude forms
Intergrating over time form an intial time `t_(i)` to a final time `t_(f)` we get
overset(i)underset(f ) (int) dp=overset(i)underset(f ) (int) Fdtg`
`P_(i)- P_(i) = underset(t) overset(t)(int) F dt`
`p_(1)=` initial momentum of the body at time `t_(i)`
`p_(f)=` final momentum of the body at time `f_(f)`
`p_(f)- p_(i) = Delta p` change in momentum of the body during the time interval
The integral `underset(t ) overset( t ) (int) F dt = j` is called the impulse and it is equal to change a in momentum of the body .
If the force is constant over the time interval then
`underset(t ) overset(t ) (int ) Fdt= F underset( t) overset( t) dt = F (t_(1) - t_(1)) = F Delta t`
`F Delta t= Delta p`
Impulse = Change in momentum