Mathematics

Problem

The height

h(t)

(in metres) of a shuttlecock above the ground

t

seconds after it is hit is modelled by

h(t)=64t^{3}-48t^{2}+12t+1.

(i) Find the expression for the instantaneous vertical velocity

v(t)

of the shuttlecock. (ii) Determine the velocity at

t=0\!\!\;\text{s}

t=1\!\!\;\text{s}

and

t=2\!\!\;\text{s}

. (iii) Comment on whether the shuttlecock is rising or falling at each of these instants, based on the sign of

v(t)