1. The problem statement I am studying for an upcoming test and I am having a lot of trouble relating velocity, acceleration, and displacement vs time. Given a position vs time function: x(t) = 6m - (8m/s)t + (1m/s^2)t^2 I cannot for the life of me understand how to find any instantaneous velocity at any time (t), the acceleration, or any time (t) that the particle changes direction. 2. Relevant equations Equations that I have been trying to use to determine the information are: The limit t->0 of Dx/Dt (Instantaneous velocity, change in position over change in time) The limit t->0 of Dv/Dt (Instantaneous acceleration, change in velocity over change in time) Or should I be focusing on the kinematic equation: X=Xi + (Vi * t) + 1/2 At^2 3. The attempt at a solution I do not even know where to start. Vectors seem so much easier than this. :( EDIT: I am going to feel very stupid if the answer is sitting in front of me like I think it is. I just noticed that the equation given to me is in the exact form of one of the kinematic equations, minus the 1/2 in front of A, does that mean that acceleration is just 2m/s^2 (2 * 1/2 * 1m/s^2)? Likewise, is the initial velocity -8m/s? If I am right on about that, the time at which the velocity reaches 0 (changes sign) would be 4 sec?