2. An earthmover which, when empty, has mass M and a material carrying capacity of V is used to spread
sand across the roadbed of the new Metro Purple line (currently under construction assuming the contractor
can stay out of jail). Initially, the earthmover is completely filled with sand which has a density of $\rho$. The
earthmover begins accelerating from rest to the left across level ground without turning while dumping sand
at a constant rate k vertically through the discharge port. As the earthmover moves, the wheels provide a
constant tractive force via friction of T to the left.
For convenience, you may assume that M has units of kg, V has units of m$^3$, $\rho$ has units of kg/m$^3$, k has
units of kg/sec, and T has units of N.
(a) Sketch the FBD of the earthmover as it accelerates.
(b) Determine the time required to discharge half the sand.
(c) Determine the acceleration of the earthmover when half the sand has been discharged.
(d) Determine the velocity of the earthmover when half the sand has been discharged.
Express your results in terms of k, M, T, V, and $\rho$ as appropriate.