Problem $3$ on stopping distance $(22$ points$)$: An engineering student is driving on a level roadway and sees a construction sign $500ft$ ahead in the middle of the roadway. The student strikes the sign at a speed of $25m\frac{i}{h}.$ If the student was traveling at $55m\frac{i}{h}$ when the sign was first spotted, what was the student's associated perception$/$reaction time $($use practical stopping distance$)?$