Problem 2. One-dimensional rectilinear motion under a conservative force. A mass m = 0.100 kg can move along the x-axis without friction. The mass is subject to a conservative force. Its potential energy is given by the function U(x) = Ulet/ + Uze x/L In this function, L = 1.00 cm, and U1 and U2 are unknown constants, to be determined in part a. At a certain time, the mass passes the origin with velocity vx = +5.00 m s" in the +x direction. It is observed to travel to x =+1.00 cm, where it comes to a standstill and reverses direction. As the charge moves in the -x direction, it is observed to reach the point with x = -3.00 cm, where it comes to a standstill and reverses direction again. a) Calculate the constants U1 and Uz. b) Calculate the position of the equilibrium position, where the net force on the mass is zero. c) If we write the velocity of the mass as U = Ur a , draw a graph of Ux as a function of x, as the mass completes a full cycle from x = -3.00 cm to x = +1.00 cm and back to x = -3.00 cm