You are late for train. When you are $80\mathrm{.}0$ m from the rear of the train, it begins to pull out of the station with a constant acceleration of $0\mathrm{.}100$ m$/$s$2.$

$($a$)$ If you run at a constant speed of$\mathrm{ 5}\mathrm{.}00$ m$/$s$,$ will you catch the train? If so$,$ how far will you have run when you reach the rear of the train? If not, how close will you get?

$($b$)$ Repeat part $($a$)$ if you are running at $3\mathrm{.}00$ m$/$s$.$

$($c$)$ What is the minimum constant speed you can run at and still catch up to the rear of the train? 

$($d$)$ Sketch the three situations on a position versus time graph $$and explain these. Explain with steps