First slide
Instantaneous acceleration
Question

Velocity is given by v = 4t (1 - 2t), then find the value of time at which velocity is maximum. 

Moderate
Solution

To find value of time at which velocity is maximum, taking differentiation of v with respect to time

                        dvdt=0

Given,              v = 4t (1 - 2t)

                         v=4t-8t2ddt4t-8t2=0 

        4-16t=0     t=14 s=0.25 s

Again, taking differentiation, we get

          d2vdt2=-16<0

So, at t = 0.25 s, velocity is maximum.

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