dP/dt questions.

Question

I know dP/dt is the instantaneous change in momentum.

How do you calculate it? Why do you need it?

Answer 1

dP/dt is the instantaneous rate of change of momentum with time, this in turn gives us a value of force. We know this because of Newton’s second law and through dimensional analysis. (kg*m/s divided by s gives units of newtons.) Conversely, the integral of force with respect to time is the impulse, or the change in momentum! Calculus ties these two phenomena together, just like in kinematics with position, velocity, and acceleration.