Oil Piston The brake mechanism used to reduce recoil in certain types of guns consists essentially of a piston attached to the barrel and moving in a fixed cylinder filled with oil. As the barrel recoils with an initial velocity vo, the piston moves and oil is forced through orifices in the piston, causing the piston and the barrel to decelerate at a rate proportional to their velocity; that is, a = -kv. Express (a) u in terms of t, (b) x in terms of t, (c) v in terms of x. Draw the corresponding motion curves.