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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?

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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.

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  • $\begingroup$ Yep, thanks. It yields 50000m/s^2, about 5100 G's. I don't think a commercial application for living things is appreciable. $\endgroup$
    – Gui13
    Commented Jul 29, 2015 at 15:34

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