I'm currently preparing for a prelim and just wondering if my solution to this problem is correct. I did a plot of v(t) and it looked reasonable. You can find the question and solution both at http://oi50.tinypic.com/2e3v4e8.jpg. The Problem states: A spacecraft of mass m_0 and cross-sectional area A is coasting with a velocity v_o when it encounters a stationary dust cloud of density rho. Assuming that all the dust sticks to the spacecraft and that A remains unchanged, find the subsequent motion, i.e. v(t) of the spacecraft. Update: I seem to have made an error by pulling v outside of the integral. Thank you all for the help.