4. 207 Car A is 100 meters west of Car B. Now both cars start moving east at the same time. If Car A moves forward at a constant speed of 50 meters/second, and Car B accelerates forward at 20 meters/second ${ }^{2}$, how many seconds will it take for the two cars to be closest to each other? At that time, how far apart are the two cars?
［Solution］ Let the distance between the two cars be $S$ meters after $t$ seconds.
At this time, car A is $S_{1}=v t=50 t$ meters from the starting point, and car B is
$$\begin{aligned}
S_{2} & =100+\frac{1}{2} a t^{2}=100+10 t^{2} \\
S & =S_{2}-S_{1}=100+10 t^{2}-50 t \\
& =10\left(t-\frac{5}{2}\right)^{2}+\frac{75}{2}
\end{aligned}$$

Therefore, when $t=\frac{5}{2}$ (seconds), $S$ is minimized, at which point the two cars are $\frac{75}{2}$ meters apart.