I always see that a ball moving in a constant speed collide with another ball is common conservation of momentum problems. Obviously, I know that the momentum is mass*velocity But, what if the ball accelerates and collides with another ball ? I think I can't use mass*velocity for the momentum because the velocity is not constant. Then, I think that I might have missed the Δ symbol. Because I think that the conservation of momentum is derived like below. F = -F m Δv/Δt = m Δv/Δt Because the object A contacts object B at the same time as the object B contacts object A, so we can cancel Δt So, m Δv = m Δv So, is the formula m Δv ? But, I doubt it, because I think non-accelerating objects which has Δv = 0 since its velocity doesn't change also have momentum Or, maybe the formula is mass times the velocity the object has when contacting another object. But, I don't know how to derive the formula (p = m*v) since F = ma = m Δv/Δt has a delta symbol and momentum formula doesn't have delta symbol. So, What is the momentum formula ? Is it mass times the velocity the object has when contacting another object or m v ? Or is it m Δv ? If the formula is m v , Please tell me how to derive that formula.