I have been searching for a straight forward answer to this question for ages now and it is driving me crazy.
Here is what I know: If an object is moving at a constant speed the force of friction must equal the applied force (Please assume the applied force is horizontal) and for it to be accelerating or decelerating, the force of friction and the applied force must be uneven.
I know that FK = uK * FN
I have the applied force, the normal force and the coefficient of friction.
This is what I do not understand: If in order to accelerate the applied force must be greater than the friction, how would that work? because surely the object would continue accelerating to infinity? Or does the friction force change to level out and equal the applied force to change the objects state from accelerating to constant velocity? If so, how do i work out the rate of the change in the friction force, surely it does not instantly change otherwise acceleration cannot occur.
Here is a sample situation that may help me understand it better if it is answered
Say I have a box that has a mass of 10 kg and I apply a force horizontally to the box of 50N and the coefficient of kinetic friction is 0.5. How long does it take for the box to finish accelerating and reach a constant velocity? And what is the rate of friction force change?
Then say I suddenly increase the force I am applying to 60N what is the rate of change of the friction force and how long does it take to reach constant velocity?
To recap my questions are: 1. Does the object accelerate to infinity or does the friction force change to equal the applied force? 2. If the friction force does change, how do I work out the rate of change and how long it takes? 3. In the situation above, both times a new force is applied how do I work out change in friction force and how long it takes? Could you also show working so I can understand it properly. 4. If the above is way off and the friction does not change how do I work out the change of velocity over time using friction depending on a change of the applied force?
Sorry for the detailed question I just want to make sure I understand the answer properly :)
PS A simple solution is all I need as I am using this in a simple physics engine for a game.