Show that impulse is the change of momentum

Explanation

According to Newton.s Second Law
`F = (dp)/(dt) ` i.e., dp = Fdt
Integrate it over a time interval from `t_i` to `t_f`
`int_(i)^(f) dp = int_(t_i)^(t_f) Fdt`
`P_f - P_i = int_(t_1)^(t_2) F.dt`
`P_i to` Intial momentum of the object at ` t_i`
`P_f to` Final momentum of the object at `t_f `
`P_f - P_i = Delta p` = change in momentum during the time interval `Delta t. int_(t_i)^(t_f) Fdt = J` is called the impulse .
If the force is constant over the time interval `Delta t` , then
`int_(t_i)^(t_f) Fdt = F int_(t_i)^(t_f) dt = F (t_f - t_i) = F Delta t`
`J= F Delta t = Delta p`