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I'm trying to approximate a velocity curve from the following parameters:

  • initial velocity
  • final velocity
  • the total displacement (the area under the velocity curve)
  • the duration of the acceleration

We assune that the curve is monotically increasing due to the acceleration.

Is there any numerical or analytical way to do that? (Look-up table or function approximation)

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Arthur
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A. Khalef
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  • Is the acceleration constant? Otherwise, do you know the behaviour of the acceleration? – Peter Foreman Mar 06 '19 at 22:10
  • If you only had the first, second, and fourth pieces of information then you would probably assume the acceleration is constant and take a straight line. Given that you also have the third piece of information, a natural idea is to take the velocity to be quadratic (assuming you know nothing about the acceleration). – Ian Mar 06 '19 at 22:11
  • Hey Peter, the acceleration is actually not constant. – A. Khalef Mar 06 '19 at 22:13
  • the acceleration profile ist actually unknown, but we may know when the maximum acceleration occurs. I'm not sure whether this could help – A. Khalef Mar 06 '19 at 22:22
  • Hey @A.Khalef, it would help to know where the max acceleration occurs. Based on the information provided so far, you could have any increasing function that connects the two points indicated and with the correct area under the curve. There are essentially infinitely many curves that would satisfy these conditions. Each additional piece of info you have will help eliminate some of the possible curves and narrow it down to be as specific as possible. – Jake O Mar 06 '19 at 22:25

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