An unmarked police car traveling a constant $90$ km$/$h is passed by a speeder traveling $125$ km$/$h$.$Precisely $1\mathrm{.}00$ s after the speeder passes, the police officer steps on the accelerator; if the police car's acceleration is $2\mathrm{.}50$ m$/$s$2,$ how much time passes after the police car is passed by a speeder and before the police car overtakes the speeder $($assumed moving at constant speed$)?$