# Calculate constant power applied to displace a mass a given distance within a given time

I'm trying to determine electric motor power sizing with requirements given for covering a particular distance within a certain time. The knowns are the vehicle mass, the allotted time, the target distance to cover, and the vehicles initial velocity. The result would be the absolute minimum possible motor output power rating that would satisfy the requirement.

• Not enough information. You need to know desired acceleration, and steady-state power to keep it moving at the desired speed. Moving an air hockey puck takes almost no energy. Moving a buggy across sand might take a lot. Jun 30, 2023 at 18:26
• @TigerGuy Not necessarily. If you assume starting with zero velocity, you could calculate minimum energy required for acceleration for some niche cases, like a very short distance. Although for more realistic scenarios, I agree with you. Jun 30, 2023 at 20:30

We calculate the acceleration of the linear motion, $$\alpha$$,then apply
$$F=m\alpha$$ To get F. and power is $$P=\frac{F*x}{t}$$ So. $$x=V_{0}t+\alpha t^2/2$$ $$\alpha= \frac{2(x-v_0t)}{t^2}$$ From this we get $$F=m* \frac{2(x-v_0t)}{t^2}$$ anf required power is
$$P =\frac{x*m* \frac{2(x-v_0t)}{t^2}}{t}= x*m* \frac{2(x-v_0t)}{t^3}$$