force produce a large change in momentum ?

Question

how can a small force produce a large change in momentum ?

Answer 1

Momentum indicates the product of a mass and velocity.
If a mass is very large if would take a lot of power to make it move at a very high velocity. Hence large masses move at slow velocity as compared to micromasses such as particles of light.
Its is the Velocity of the force that would produce a large momentum. So a small mass must be given a lot of power to cause it to move would have a high velocity.
A large mass Given the same power would have a large force but a very small velocity for the same momentum as the small mass.

If you push a car from a point of standstill,you initially have a large force and zero momentum.As the cars starts to move the force disminishes and as the velocity of the car increases to a limit the force dwindles to almost zero. At that point the car would move for ever at that velocity if the friction (resistance to the motion)was zero. And the momentum would remain constant.
However because of a large friction force exists between the road and the tires.Even though there is a large force between the car and the tires ,the momentum would eventually dwindle down to zero.
The car would only move again if only additional power is applied to the car.

Answer 2

Force = (final momentum - initial momentum) / time taken,
so
Force x time = change in momentum

So if a small force acts over a very long time period, you will get a large change in momentum.