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The engine of a car is developing a power of 90kW when it is moving on a horizontal road at a constant speed of 100 km h−1. Estimate the total horizontal force opposing the motion of the car.

I plugged in the values to get $F = 3240 N$, but am struggling to understand what this means. I know the derivation of the formula, and it makes perfect sense to me, but conceptually I am struggling to grasp this equation.

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  • $\begingroup$ power (W) = force (N) $\times$ velocity (m/s). $\endgroup$
    – Farcher
    May 5, 2016 at 10:18
  • $\begingroup$ I'm voting to close this question as off-topic because it shows insufficient prior research $\endgroup$
    – garyp
    May 5, 2016 at 10:37

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From the definition of work $$W = \int dx F$$ and $$P = \frac{dW}{dt}$$ you can see how we can arrive at $$P = F \frac{dx}{dt} = F v$$ (when considering only the absolute value).

To understand it intuitively, imagine the case of a frictionless system in which the car can move at a certain speed without any opposing force. The power required to keep it at this speed will be zero, because no energy dissipates through friction.

On the other hand, if we add friction, energy is given off to the surroundings and therefore the kinetic energy of the car decreases. Using $$v = \sqrt{\frac{2E_{kin}}{m}}$$ also the speed of the car decreases. To counteract this acceleration, the car needs to output power $$P = F v$$

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