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Maths_Teacher

- 6

- 0

The questions were in relation to problems involving a car being propelled by some kind of engine and experiencing a constant external resistive force.

In this situation the equation Power = Driving Force x Velocity is used. If the power output of the engine is constant then this implies the Driving Force starts at a maximum value and gradually reduces as the velocity increases until the car reachs a maximum velocity and the car stops accelerating. At this pointy the driving force must be equal to the resistive force. When challenged I struggled to explain why the driving force is varying and further why is should start at a high value and then reduce (if anything it seems it should be the other way round). I tried to think in terms of the work done by the engine with some being converted to kinetic energy, as well as heat and sound, but this didn't help.

This all got me thinking about the derivation of P=Dv I’ve always done this by differentiating work (written as force x distance) stating the force is assumed constant. However, in the example above it seems clear that D is some kind of function of t!

I then started thinking about Power in terms of energy transfer and noted that for an idealised system where all work done by an engine is converted to Kinetic Energy, taking the rate of change of KE leads to the same formula (P=DV). So is the above due to some kind of implied modelling assumption?

Can anybody help with a better explanation I can offer my inquisitive sixth formers.