A puck of mass m moving at speed v on a horizontal, frictionless surface is stopped in a distance d because a hockey stick exerts an opposing force of magnitude F on it. If the stopping distance d increases by 58 %, by what percent does the average force needed to stop the puck change, assuming that m and v are unchanged?

-36.71%

Explanation:

Using the Generalized Work Energy Principle, the puck is brought to rest by an external force and the system has no kinetic energy

#Denote the stopping distance and force required with a prime and observe from (i) that:

 #If stopping distance increases by a factor of 79/50;

So F decreases by 36.71% . we expect force to reduce since the same amount of work is repeatedly done on the system over a long distance.