A cart of initial mass M0 moves along a frictionless horizontal track with speed v0. Starting at t=0, fine sand with negligible horizontal velocity relative to the ground pours vertically into the cart at a constant rate r (in kg/s). Neglect any sand loss after it lands. Which expression gives the cart's speed v(t) at time t?
a) v(t)=v0M0M0+rt
b) v(t)=v0e−rt/M0
c) v(t)=v0M0+rtM0
d) v(t)=v0M0+rtM0