1. The problem statement, all variables and given/known data An engineer designing a system to control router for a machining process models the system so that the router's acceleration (in in/s2) during an interval of time is given by a= -0.4v, where v is the velocity of the router in in/s2. When t=0, the position is s=0 and the velocity is v= 2 in/s. What is the position at t=3 seconds? 2. Relevant equations a= dv/dt 3. The attempt at a solution This section has to do with straight line motion when the acceleration depends on velocity or position. This is what I tried to do: a= -0.4v a= dv/dt dv/dt = -0.4v dv/v= -0.4 dt I integrated both sides and I got: ln v = -.4t + C ( C = constant) From my differential equations math class, we did problems like these and we got rid of the ln by making it all a power of e. eln v = e -.4t + C you get v= e-.4t+C or v= e-.4tC Now I know this is wrong because we know that when t=0 v=2. Am I on the right track or did i do this completely wrong? Thanks for any help.