Question

modifying momentum
while riding a bicycle, a small animal stops in your path.
what is the best way to decrease the force you experience while slowing to a stop?
apply a large force to the brakes over a short period of time.
apply a small force to the brakes over a longer period of time.
there is no way to decrease the force that you will experience.

Explanation:

To decrease the force experienced while slowing down, we use the impulse - momentum theorem, which states that the change in momentum $\Delta p$ is equal to the impulse $J$, and impulse is also given by the product of force $F$ and time $t$ ($J = F\times t=\Delta p$). The change in momentum when stopping the bicycle will be fixed (since we go from a moving state to a stopped state). If we want to decrease the force $F$, we can increase the time $t$ over which the force is applied (because $F=\frac{\Delta p}{t}$). Applying a small force over a longer period of time increases the time $t$, which in turn decreases the force $F$. Applying a large force over a short period of time would increase the force, and the statement that there is no way to decrease the force is incorrect.

Answer:

Apply a small force to the brakes over a longer period of time.