Power is the rate of doing work , that is the work done per second, usually by the driving force of an engine. It is a scalar quantity and can only be positive.

International A Level (IAL)MathsEdexcelMechanics 2FlashcardsWork, Energy & PowerPower

Power (Edexcel International A Level (IAL) Maths: Mechanics 2): Flashcards

Exam code: YMA01

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Define power.

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Define power.
Power is the rate of doing work, that is the work done per second, usually by the driving force of an engine.
It is a scalar quantity and can only be positive.
A driving force of $F$ N acts on an object moving at $v {m s}^{- 1}$ , doing $WD$ joules of work in $t$ seconds. Fill in the blanks to complete the two formulae for power:
$P = \frac{______}{t} =______$
The completed formulae are:
$P = \frac{WD}{t} = F v$
The second form is the more useful in vehicle questions, and it requires the velocity to be in the same direction as the force.
True or False?
The force in $P = F v$ is the resultant force on the vehicle.
False.
It is the driving force of the engine alone, since power is what the engine develops as it converts fuel into that force.
The resistance forces belong in the equation of motion, but they must be kept out of this formula.
How is $P = F v$ obtained from $P = \frac{WD}{t}$ ?
The work done by a constant force $F$ over a distance $s$ is $F s$ , so the power is $\frac{F s}{t}$ .
Since $\frac{s}{t}$ is the speed $v$ , that is simply $F v$ .
What are the units of power?
Watts (W), where 1 watt is 1 joule per second.
Larger powers are given in kilowatts, with $1 kW = 1000 W$ , so check which the question wants before giving an answer.
Why does a vehicle working at maximum power eventually reach a maximum speed?
With $P$ fixed at its maximum, $P = F v$ means the driving force falls as the speed rises.
Eventually the driving force has fallen to equal the resistance, so the resultant force is zero.
By Newton's second law the acceleration is then zero, and the speed stops increasing.
A car of mass 1300 kg meets a constant resistance of 900 N and has a maximum speed of $40 {m s}^{- 1}$ . Find its maximum power, and say why the mass is not needed.
At maximum speed the acceleration is zero, so the driving force equals the resistance, 900 N:
$P = F v = 900 \times 40 = 36000 W = 36 kW$
The mass is not needed because zero acceleration makes $m a$ zero, so the mass never enters the equation of motion.

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