The horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. If the velocity of the plunger is v0 in the position x where x = 0 and t = 0, and if the deceleration is proportional to v so that a = -kv, derive expressions for the velocity v and position coordinate x in terms of the time t. Also express v in terms of x. Solve by using numerical analysis in excel. Use values : V0 = 0.5 m/s and k = 4/second