Mathematics

Problem

The height (in metres) of a ball thrown vertically upward is modelled by

h(t)=2t^{3}-9t^{2}+12t+4

for

0\le t\le4

, where

t

is the time in seconds after the ball is released. a. (i) Obtain the velocity function

v(t)

. b. (ii) Find the instantaneous velocity of the ball at

t=2\,\text{seconds}

. c. (iii) Determine the value(s) of

t

in the interval

0\le t\le4

at which the ball is momentarily at rest.