From Mechanics
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From part a)
\displaystyle v=2kt-5{{t}^{2}}
Thus
\displaystyle \begin{align}
& 0=2k\times 20-5\times {{20}^{2}} \\
& 0=40k-2000 \\
& k=\frac{2000}{40}=50 \\
\end{align}
