please explain me mathematically that the speed of a driving car safely in darkness depends upon the range of headlights.
The only hint which I got was that:-I the range of headlight is x and the driver if spots a obstacle at the distance of x,and he produce retardation of 'a'.then the distance covered by car before stopping.
please help me I was not able to make head or tale of hint.solve it mathematically

For safe driving the driver must be able to react to hazards in the road to avoid hitting them. If he is driving at speed 'V,' and if his reaction time is 'T,' then the distance traveled before he's able to react is V times T. The distance must be less than the headlight distance, or else he won't be able to avoid a collision. So if 'H' is headlight distance then H> VT, which can be rearranged to V < H/T.