From Mechanics

\displaystyle \begin{align} & v=\int{adt} \\ & \\ & =\int{\left( -kt \right)dt} \\ & \\ & =-\frac{k{{t}^{2}}}{2}+c \\ & \\ & t=0,\ v=20\ \Rightarrow \ c=20 \\ & \\ & v=20-\frac{k{{t}^{2}}}{2} \\ & \\ & \text{ Using}\quad t=40,\ v=5\quad \text{gives} \\ & \\ & 5=20-\frac{k\times {{40}^{2}}}{5} \\ & \\ & 800k=15 \\ & \\ & k=\frac{15}{800}=\frac{3}{160} \end{align}

Note that substituting for \displaystyle k and \displaystyle c in the expression for \displaystyle v we get

\displaystyle v=20-\frac{3{{t}^{2}}}{320}