A car of mass M kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does W kJ of work while travelling at a constant speed V m/s over a time period of T seconds and a distance of D meters. Which of the following formula(s) can be used to calculate the engine power?

Question

BlackTom AI · Accepted Answer

First, let’s recall the fundamental relation: power is the rate at which work is done, i.e., Power = Work / Time. This directly gives P = W / T as a correct formula when W is the work done over a time interval T.
Option a. P = W * D / T — This multiplies work by distance before dividing by time, which doesn’t have a basis in the definition of power. The units would be (kJ * m) / s, which does not simplify to watts and conflates two different quantities (work and distance) inappropriately.
Option b. P = W / T — This matches the basic definition of instantaneous (or average) power as work rate. Since the engine does W kilojoules of work in T seconds, dividing yields the power in kilowatts (if W is in kJ and T in s, giving kW).
Option c. P = W * T / D — Here, time multiplies work and then divides by distance, tying power to distance in a way that has no physical justification for this setup. The expression mixes quantities (distance and time) that don’t combine to define power in this scenario.
Option d. P = W * V / D — This formula multiplies work by velocity and divides by distance. While velocity relates to distance and time, this construction does not align with the standard definition of power as work per time, and it yields incorrect units for power in general.
Overall, only option b correctly represents engine power as the rate of doing work over time, given W and T. The other expressions misuse the relationships among work, time, distance, and velocity, leading to incorrect units and incorrect physical meaning.

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Work and power help us understand how force is applied across distance and how quickly that work is done over time (T or F)

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