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[itex]A = P*\Delta t[/itex]

P - power, A-work, [itex]\Delta t[/itex] - time interval.

[itex]\Delta t[/itex] and P are known (calculations are performing by discrete time steps).

Now, I want to calculate force F, that will produce car's moving. I.e. I need some function [itex]F=tadam(A)[/itex].

My attempts to solve

If motor will change only kinetic energy [itex]E_k[/itex], calculations can be like this (assuming, that body not moving yet, i.e. [itex]v_1 = 0[/itex]):

[itex]A = \Delta E_k = m*v_2^2/2 - m*v_1^2/2 = m*v_2^2/2[/itex]

[itex]v_2 = \sqrt{2*A/m}[/itex]

[itex]a = \frac{v_2-v_1}{\Delta t} = \frac{v2}{\Delta t} = \frac{\sqrt{2*A/m}}{\Delta t}[/itex]

[itex]F = m*a = \frac{m*\sqrt{2*A/m}}{\Delta t} = \frac{\sqrt{2*A*m}}{\Delta t}[/itex]

If motor will change only potential energy [itex]E_p[/itex], calculation can be like this:

[itex]A = \Delta E_p = m*g*\Delta h[/itex]

[itex]A = F*\Delta h[/itex]

[itex]F = m*g[/itex]

But, these calculations are not that I need, because I feel, that F should not depend on mass. What difference for motor, which mass has the car? I think, that force should be equal in any case. Is my feeling wrong? Why?

**Context**: I am developing a game, using physics engine Box2D. There I know motor power, and need force, that I will apply to the car body, by call

Code:

`car->applyForce(force)`