Power is the rate at which a force does work, that is the work done per second. It is a scalar , it is measured in watts , and one watt is one joule per second.

True or False? A car travelling at constant speed on a level road has an engine that is doing no work.

False. The driving force is still moving the car forwards, so it is still doing work, at a rate equal to the engine's power output. What stays the same is the car's kinetic energy, because all of that work is going into overcoming the resistance.

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Power (Cambridge (CIE) A Level Maths: Mechanics): Flashcards

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Define power.

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Define power.
Power is the rate at which a force does work, that is the work done per second.
It is a scalar, it is measured in watts, and one watt is one joule per second.
Fill in the two formulae for power:
average power $= \frac{______}{time taken}$
and, for a force acting in the direction of motion, $P =______$
Average power $= \frac{work done}{time taken}$ , and for a force acting in the direction of motion, $P = F v$ .
The first gives an average over an interval of time, while $P = F v$ gives the power at the instant the speed is $v$ .
Which force is used in $P = F v$ ?
The driving force of the engine, not the resultant force and not any resistance.
It is worth labelling it $D$ on a diagram, since $F$ is already the resultant force in $F = m a$ and is also the usual letter for friction.
Why does a vehicle working at maximum power eventually stop accelerating?
Because $P = D v$ with $P$ fixed means the driving force falls as the speed rises.
Once it has fallen far enough to equal the total resistance, the resultant force is zero, so the acceleration is zero and the speed can rise no further.
A car of mass $1300 kg$ meets a constant resistance of $900 N$ and has a maximum speed of $40 {m s}^{- 1}$ . Find the maximum power of its engine.
At maximum speed the acceleration is zero, so the driving force equals the resistance, $900 N$ .
The maximum power is therefore $900 \times 40 = 36000 W$ , or $36 kW$ .
The mass is not needed, since neither formula for power involves it.
True or False?
A car travelling at constant speed on a level road has an engine that is doing no work.
False.
The driving force is still moving the car forwards, so it is still doing work, at a rate equal to the engine's power output.
What stays the same is the car's kinetic energy, because all of that work is going into overcoming the resistance.
A car climbs a hill at a known speed, working at a known power. How do you find its acceleration at that moment?
Use $P = D v$ to find the driving force at that instant, then apply $F = m a$ along the slope.
The resultant force is the driving force minus the resistance and minus the component of the weight down the slope, and dividing it by the mass gives the acceleration.

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