# Calculate the time to travel a distance with acceleration

Hi,

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 + 1/2at2

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'

## Answers and Replies

Doc Al
Mentor
I have the formula: d=vt + 1/2at2

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
I think you mean t = √(2d/a). Parentheses matter.

Is that correct?
Not exactly. That formula is good for the accelerated part of the motion, but what about after the train achieves top speed? At that point it's just constant speed motion.

So break it up into two parts: accelerated part and constant speed part.

For the first part, ask yourself: How long does it take to reach top speed? How far does it get in that time?

For the second part, ask yourself: How much distance remains? How long does it take to travel that distance?