Increasing speed, distance, and time.

[Mantikore]

I know to find the time it takes to travel a distance, you divide the distance by the speed.. but what if you have an increasing speed?

Say I wanted to travel 5 miles.. and I start off at 0 mph and by the time I reached the 5 mile mark, I would be traveling at 40 mph and there was a steady increase. Meaning at 1 mile I would be traveling at 8 mph, at 2.5 miles I'd be traveling at 20 mph, and at 4 miles I'd be traveling at 32 mph.

Is there an equation that could tell me how long it would take to travel that distance with a steadily increasing speed?

 

[mathman]

If the acceleration is constant (as you seem to be implying) then the equation you want is $d=\frac{at^2}{2}$ were d is distance, t is time, and a is acceleration.