1. A person is chasing a car stopped at a traffic light at a constant speed of $6 \mathrm{~m} / \mathrm{s}$. When he is $25 \mathrm{~m}$ away from the car, the traffic light changes from red to green, and the car starts to move with a uniform acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$. Can this person catch up to the car?
1. Suppose the car starts moving at point $C$, while the person passes through point $A$ at the same time. After $t$ seconds, the car reaches point $D$, with $C D=\frac{1}{2} a t^{2}$. The person, at this time, reaches point $B$, with $A B=v t$. According to the problem, the distance between the person and the car is $y=A C+C D=A B=25+\frac{1}{2} a t^{2}-$ $a t=\frac{1}{2}(t-6)^{2}+7 \geqslant 7$, which means the person cannot catch up with the car, and the closest distance between them is $7 \mathrm{~m}$.