Relationship between velocity and momentum change [closed]

Question

I'm trying to understand the scenario below:

If a car travelling at 20km/h hits a person, vs if the same car travelling at 30km/h hits a person, the latter situation will obviously apply more force on the person.

Since force is proportional to the rate of change of momentum $dp/dt$, and momentum is conserved, does it follow that the car travelling at 30km/h has a greater rate of change in momentum during the collision, in comparison with the car travelling at 20km/h?

If this is true, does it follow that objects at higher velocities experience greater rates of changes in momentum during collisions?

would love some clarity on this. thanks.

Answer 1

Yes, your intuition is right. Since the person struck by the faster car will receive a greater force from the impact than the other person does, they will experience a greater acceleration that results in a greater momentum. Since momentum is conserved, this means that the fast car lost more momentum than the slow car did.

The force of an impact increases with the speed.

Do be mindful that in a realistic scenario, the driver will slam the brakes. That introduces an additional force to the situation.