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I'm trying to find out the time it takes to travel a known distance, but with a capped speed.

For example, let's say a train has an acceleration rate of 0.8m/s/s, and a top speed of 72km/h, ie: 20m/s. It's going to make a 12km journey, accelerating to it's top speed from rest. How long does it take?

I have the formula: d=vt +

^{1}/

_{2}at

^{2}

where v = initial velocity, in this case 0. d = distance, a = acceleration.

I'm having trouble making "t" the subject. Because the train is starting from rest, with an initial velocity of 0, I'm ignoring that part of the equation entirely. I came up with this:

t = (√2d)/a

Is that correct?

Thanks in advance.

Nige'