What is the relationship between the momentum of the system and the velocity of the railroad cart?

Question

I am in a Physics class and I need to get an answer for this question. Can somebody please help me out?

Answer 1

John is correct. You should also note that p = mv; where both p, the momentum, and v, the velocity, are vectors. They both have magnitude and direction. In fact, the directions of both are the same.

You should also note dp/dt = m dv/dt + dm/dt v; so that if the mass is fixed, meaning dm/dt = 0, we have dp/dt = m dv/dt = m a; where dv/dt = a which is acceleration and that is also a vector. As dp/dt = m a, we can see the change in momentum over time (dp/dt) is force. Recall f = ma? And force, too, is a vector.

So, if the velocity of that railroad car were to change (dv/dt <> 0), there would be a net force on it causing that change in velocity. And that force is just a change in momentum over time.

Answer 2

It's extraordinarily simple once you consider the definition of momentum. Momentum = Mass * Velocity.

Thus the greater the magnitude of the velocity, the greater the magnitude of the momentum of the system. (Note that i say magnitude because it is entirely possible to have a negative velocity).