I know this might be kind of an easy question but I'm just getting back into physics for school. I'm looking to take an object moving through space with an initial velocity vector, V0, and an initial position, X0, in 3D space. I'm looking at a way to get to another position, X1, and at time t when I get there, my velocity is 0. I've come up with the following equations but am a little stuck on the best way to solve...(Some sort of estimation since they are non-linear equations with more variables than equations). It seems that there might need to be some point in between t0 and t where the acceleration vector would need to be changed in order to acheive zero velocity at X1 so I've included that in these equations X1 = X0 + V0t + 1/2(A1*t1^2) + 1/2(A2 * (t - t1)^2) 0 = V0 + 2*A1*t1 + 2*A2*(t-t1) X1,X0,V0 are known |A1| = |A2| and are known I'm just looking for some advice as to a next step in coming up w/ t1, t, and the direction for A1 & A2 in order to make these equations work. Thanks for the help.