Increasing speed, distance, and time.

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SUMMARY

The discussion focuses on calculating the time required to travel a distance with increasing speed, specifically when acceleration is constant. The formula provided, d = (at²)/2, where d represents distance, t represents time, and a represents acceleration, is essential for solving this problem. The example given involves traveling 5 miles, starting from 0 mph and reaching 40 mph at the end, with specific speeds at various distances. This equation allows for determining the time taken to cover the distance under these conditions.

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Mantikore
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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?
 
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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.
 
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