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.
Ben
Best Answer
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:
$v_{max} = \frac{d}{a+d}(aT+v_0)$