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The question is: Why must the driving force on the car increase to keep the acceleration constant? If the car is accelerating the driving force is greater than friction and the resultant force is in the direction of the forward force. To keep this resultant force the same, cant we just keep the driving force the same, why does it have to be increased? I am really confused.

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  • $\begingroup$ Are you confusing force with power? Remember the power requirement goes up as $P = F\,v = m v a$. $\endgroup$ Commented Mar 6, 2020 at 13:36

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If the car is accelerating in the same direction as its velocity, then its velocity is increasing. In order to keep the acceleration constant, the net force must be constant. Since air resistance is acting on the car and increases with velocity, the driving force must also increase to counteract that.

If we were to consider the case where there was no air resistance and only friction (which is not velocity dependent), then you could simply have a constant driving force, but because air resistance does significantly affect cars, this is not the case.

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  • $\begingroup$ isnt the velocity increasing because of the driving force? $\endgroup$
    – borns
    Commented Mar 5, 2020 at 21:59
  • $\begingroup$ @borns the velocity is increasing because of the acceleration, as acceleration is defined as the rate of change of velocity. The driving force determines what the acceleration is by $\vec F_{net} = m \vec a$. $\endgroup$
    – Sandejo
    Commented Mar 5, 2020 at 22:46

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