Stopping in a small amount of time means the force must be very small

Answer 1

...but for a very large mass, it would take a correspondingly large amount of force to stop it in a short amount of time. Think of trying to stop an oncoming semi or jet airplane. A small amount of force would not stop the truck or airplane in a short distance.

The relationship between stopping distance and time depends on the mass AND the amount of stopping force, not just on the amount of force applied.

Another way to look at this: the equation for change in velocity and constant acceleration:

v = v₀ + at

Where a = acceleration (in this case, braking), t is time, v is final velocity, and v₀ is initial velocity. If we assume v = 0 (stopped), we can solve for t:

at = -v

t = -v/a

Substituting f=ma, or a=f/m:

f=ma

a=f/m

t = -v/(f/m)

t = -vm/f

Thus: stopping time is proportional to both force and mass, not just to force applied.

Answer 2

For any given mass, to stop it in a small amount of time, as opposed to a large amount of time, would require a larger force. This is mathematically illustrated by Newton's Second Law of Motion:

 ΣF = ma

The sum of all the forces acting on a system is equal to the mass of the system multiplied by its acceleration. Thus, to stop a system in motion faster (decelerating it to 0 m/s), requires a GREATER amount of force, for any given mass.