A stone is thrown vertically down from a high building with an initial velocity of $4\;\mathrm ms^{-1}$. Calculate the time required for the stone to travel $30\;\mathrm m$. So far I have tried using the SUVAT equation $$s = ut + \frac12at$$ Using this:
$$\begin{align} u &= 4\\ s &= 30\\ a &= 9.8\\ t &= ?\\ 30 &= 4t + \frac12(9.8)t\\ 30 &= 4t + 4.9t\\ 30 &= 8.9t\\ t &= 3.37s\end{align}$$
According to my book that is incorrect, but I'm not sure where I have gone wrong and would appreciate any help. Thanks.
It should be $0.5 at^2$ instead of $0.5at$. Hence a quadratic equation.
Note this comes from the fact that the acceleration $s''$ is equal to $a=9.8$. Then integrated twice.