While on a trail, a mountain biker encounters a sandy patch that is 7.1 m long. The speed of the bike entering the patch is 10.1 m/s. If the force exerted by the sand on the bike/biker system (103.8 kg) is 514 N, determine the speed of the biker when exiting the sandy patch.

Answer 1

Subtract the work done moving through sand (force x distance) from the initial kinetic energy. That will be the final kinetic energy,
(1/2)M Vfinal^2

Then solve for Vfinal.