A Porsche starts from rest at time t 0 During the first 20

A Porsche starts from rest at time t = 0. During the first 20 seconds of its motion, its velocity in km/h is given as a function of time by v = 22.8t - 0.88t^2, where t is in seconds. What distance in km does the car travel during the 20 seconds?

Solution

Car\'s max. speed occurs when dv/dt=0.

V(t)=22.8 t- 0.88t²

dv/dt=22.8-2 X 0.88 t=0

t=22.8/(2 x 0.88)

t=12.95 s

speed max at t=12.95 s

max speed is = 22.8 X 12.95- 0.88 X 12.95 X 12.95

=147.68 km/h ( problem statement says v in km/h and t in s)