# Calculate constant acceleration for a length of track with start at rest and final velocity known [closed]

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?

## closed as off-topic by ACuriousMind♦, Kyle Kanos, John Rennie, HDE 226868, Rob JeffriesJul 29 '15 at 21:04

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• It's a system of two equations and two unknowns. This isn't a physics difficulty. It's an algebra difficulty. – Bill N Jul 29 '15 at 14:13
• – Kyle Kanos Jul 29 '15 at 14:26
• Bill : figured that out ... my algaebra must be rusty too.. – Gui13 Jul 29 '15 at 15:36

## 1 Answer

There are 4 standard kinematic equations from Newtonian mechanics, and you need what is usually considered to be the fourth equation.

$\mathrm{(final\ velocity)^2 = (initial\ velocity)^2 + 2 \times acceleration \times distance}$

You know the initial velocity, final velocity, and distance. Solve for acceleration.

• Yep, thanks. It yields 50000m/s^2, about 5100 G's. I don't think a commercial application for living things is appreciable. – Gui13 Jul 29 '15 at 15:34