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I want to simulate the horizontal motion of a vehicle driven by an engine of given power P. For start in the simplified case with no friction (no dissipative forces).

My problem is with P = Fv: Suppose the vehicle was launched backwards with an initial velocity -v0 while the engine pushes forward -- it will decelerate, stop, and then reverse direction. When the vehicle changes direction v = 0, so if I calculate the force F = P/v I get infinity.

I asked an AI assistant and it said to limit the magnitude of the force. But it doesn't work nicely, the force graph still has a weird shape around the stopping point.

I need the force for the case when I introduce drag: F_acceleration = F_engine + F_drag, where F_drag = - k*v. My goal is to simulate a very simple vehicle with an interactive "acceleration pedal" (gas pedal), to show that it does not control the acceleration of the vehicle.

What is the customary way of dealing with this 'infinite force at rest` problem in numerical simulations (an ODE solver)?

Amenhotep
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1 Answers1

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Your required force is NEVER infinite.

$$F={\frac P v}$$

is valid when $v=constant$.

Otherwise, $F=m \times a $ is dominant, where a is the acceleration at that instant.

($F= m \times a + {\frac {dm} {dt}} v$ , to be exact) .

As nowhere the direction of acceleration changes during the retardation part, $v$ clearly is not constant but we can assume $a$ is. If $a$ is function of time, then use calculus and derive the above. I hope that resolves the conflict of infinite force.

Edit:- The OP had some doubts regarding this so let's clear it. First of all you need to know the mass of the vehicle. Knowing the power is useless as we know that displacement is zero. So, literally force can be anything. You are actually trying to find an answer to an equation with 2 variables with only one equation. If you don't know the mass. I'm sorry, friend, you can't the calculate the force, considering the data, you mentioned in the comment.

Ritzthephysibeast
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