We know from 2nd law of motion that $$\vec{F} = \frac{d\vec{p}}{dt}.$$
Now, a rate of change can be instantaneous. So, rate of change of momentum is instantaneous. butBut I doubt how can there be change of momentum at an instant?
But when it comes to impulse, it always acts for a certain time, however small (infinitesimal) it might be. If rate of change of momentum is instantaneous and force is instantaneous, why can't the impulse be instantaneous? What is the cause?
Can anyone also tell how can there be change of momentum at an instant?