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**Pulsar06** Right... as Jhevon said, to maximize or minimize any function, take its derivative, find its critical values and examine the its increasing/decreasing behavior. You obviously know how to maximize velocity since you explained the process in the original post. To maximize acceleration, take the third derivative of position (or first derivative of F''), which I think is known as 'jerk' (but don't quote me on that), set it equal to zero, and use the same process. There is a slight difference though: F'' = 32 so F''' = 0 (i.e. the object is neither accelerating or decelerating). The max acceleration is therefore 32 m/s^2.