Try to imagine a situation in which the form f=ma would no apply, but the form f=delta p / delta t could be used. Describe that situation. How could you test your prediction.

Answer 1

Could this be a possible answer for the above question.

When catching a ball with bare hands hurts, because it has some force. Since the the ball will always approach one at the same speed, therefore its change in momentum deltaP= Vfinal - Vinitital where Vfinal is zero.
Thus if you allow your hands to move in with the ball as you catch it, you increase the contact time and the total force will be less and hurts less on bare hands.

Answer 2

Since p = mv,

f = dp/dt is equivalent to f = m dv/dt = ma, if the mass is constant

However, mass IS constant for a closed system; so I can't imagine situation with f not equal to m*a.

Answer 3

Total force required to catch a ball is indeed less if you decelerate slowly with a longer contact time. But you have decreased a to decrease f.

f still equals m a

Answer 4

Could the question be true when the mass is not constant, say maybe in the case of cars.

When two cars collide, their masses change but their resultant momentum would be the same before and after the crash so you could you delta p, and the time.

Would that be a possible answer?