Question

How to find maximum acceleration from velocity equation using calculus

Answer 1

It is similar to finding of the maximum value of a function. Suppose you are given velocity as a function of time V(t). Differentiate it with respect to t. You will get acceleration function A(t). To find at what time acceleration is maximum, A(t) has to be differentiated with respect to t and equalize it with zero i.e. d(A(t))/dt = 0. After solving the equation, we'll find the values of t. Now these t values are the values of time where acceleration may be maximum or minimum.

Now differentiate d(A(t))/dt with respect to t. You will get d(d(A(t))/dt)/dt. Now put the values of t which you got while solving d(A(t))/dt = 0 in d(d(A(t))/dt)/dt. For which value of t the value of d(d(A(t))/dt)/dt becomes negative, at that t, you will get the maximum acceleration. Now put that value of t in A(t), and you will get the maximum acceleration.