Answer
$$11.1 s$$
Work Step by Step
\begin{aligned}
&v_{S p \text { reder }}(t+0.800 s)=x_{S p e c d e r}\\
&=>(42.0 \mathrm{m} / \mathrm{s})(t+0.800 \mathrm{s})=x_{S p \operatorname{ped} e r}\\
&v_{0, \text { Policecar }}(0.800 s)+v_{0, \text { Police }} \operatorname{car} t+\frac{1}{2} a t^{2}=x_{\text {Police car }}\\
&=>(18.0 \mathrm{m} / \mathrm{s})(t+0.800 \mathrm{s})+(18.0 \mathrm{m} / \mathrm{s}) t+\frac{1}{2}\left(5.00 \mathrm{m} / \mathrm{s}^{2}\right) t^{2}=x_{\text {Police } ~ c a r ~}\\
&\text { The two displacements equal }\\
&==>(42.0 \mathrm{m} / \mathrm{s})(t+0.800 \mathrm{s})=(18.0 \mathrm{m} / \mathrm{s})(0.800 \mathrm{s}) t+\frac{1}{2}\left(5.00 \mathrm{m} / \mathrm{s}^{2}\right) t^{2}\left(2.50 \mathrm{m} / \mathrm{s}^{2}\right) t^{2}-\\
&(24.0 \mathrm{m} / \mathrm{s}) t-19.2 \mathrm{m}=0\\
&t=\frac{-(-24.0 m / s) \pm \sqrt{(-24.0 m / s)^{2}-4\left(2.50 m / s^{2}\right)(-19.2 m)}}{2\left(2.50 m / s^{2}\right)}\\
&=>10.3 \mathrm{s}=t
\end{aligned}
