Suppose I was asked to find the Maximum acceleration of particle given the equation:
s(t) = -16t^2+7t+2
I know that
v(t) = -32t+7
a(t) = -32
But how would I Maximize it? I know that when it comes to velocity I would just take the derivative of the given s(t) equation, then set that velocity v(t) equation equal to zero and solve for t. Then I would plug in that t value in the the original s(t) height equation; however I am unsure as to how I would go about doing this for acceleration. I know that F'' aka the acceleration double derivative deals with concavity. Would the best method be to set up a test line then test values below -32 and above -32 to see whether it is concave up or concave down. I guess that I would also have to test -32 to see whether or not it would be equal to. I am just wondering how I would go about "Maximizing Acceleration". Please let me know when you all get a chance. As always I appreciate all of your help and insight.