For a motor application I wan't to be able to find the maximum velocity I should ask my motor to use knowing:

  • Distance to go D
  • Time to travel T
  • Acceleration a
  • Deceleration d
  • Initial velocity v0

So that my motor will go from initial position p0 with initial velocity p0 to final position with velocity = 0.

I found several post doing it the other way. Solving for time given maximum velocity. And I have a hard time reversing the equation.

Thank you for your help.


  • $\begingroup$ Can you write down the solution for time given maximum velocity? If possible, do it by editing your post and using MathJax. The link for reference is here: math.meta.stackexchange.com/questions/5020/… $\endgroup$ – 5xum Nov 13 '18 at 9:23

If the vehicle accelerates from velocity $v_0$ to velocity $v_{max}$ over a time $T_1$, then we have

$T_1 = \frac{v_{max} -v_0}{a}$

If it then decelerates from velocity $v_{max}$ to rest over a time $T_2$, then we have

$T_2 = \frac{v_{max}}{d}$

We know that the total time $T$ must equal $T_1+T_2$, so

$T = \frac{v_{max} -v_0}{a} + \frac{v_{max}}{d}$

Re-arranging this to solve for $v_{max}$ gives:

$v_{max} = \frac{d}{a+d}(aT+v_0)$

  • $\begingroup$ Thank you for your help! $\endgroup$ – I33N Nov 14 '18 at 20:24

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