My maths and physics are rusty... I'm a bit ashamed, but I have this problem:

Let's have a 1000m linear accelerator (mass driver) propel a payload at constant acceleration, with a final velocity of 10km/s.

What I can't figure is how to calculate the necessary acceleration given these data.

I know that:

• $v(t) = a * t$
• $x(t) = \frac 12 * A * t^2$
• A is constant.

With all initial conditions at 0 (no speed, no acceleration, payload at the entry of the tube). All these equations take time as a parameter, whereas I don't know the time it takes, since I only have the final velocity.

How do I solve this?