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

Begin by identifying the fundamental relationship involved: power is the rate at which work is done. The general formula is P = Work / Time.
Option a: P = W * D / T. Here W is energy (kJ) and D is distance (m). Multiplying energy by distance and then dividing by time yields units of kJ·m/s, which do not correspond to power (which should be energy per unit time, e.g., kJ/s or W). This option mixes quantities in a way that does not match the dimensional analysis of power.
Option b: P = W * V / D. This expression combines work with velocity and distance in a way that produces units that are not consistent with power. Specifically, W has units of energy, V is m/s, and D is m; the resulting units would be energy·(m/s)/m = energy/s, which superficially resembles power, but the derivation is not valid from the given data, since there is no basis to multiply by velocity and divide by distance for power in this context.
Option c: P = W / T. This aligns with the standard definition of electrical/mechanical power as energy transferred per unit time. Since the engine does W kilojoules of work over T seconds, the average power output is W divided by T, with units of kJ/s (which can be converted to watts).
Option d: P = W * T / D. Here you multiply energy by time and divide by distance, yielding units of kJ·s/m. That does not match the units of power, and conceptually it mixes the transport of work over a distance in a way that does not reflect the rate at which work is done.
Additionally, the problem states the speed is constant, which would imply the engine’s work over time is directly tied to energy transfer rate, supporting the familiar P = W / T form rather than any expression that involves multiplying by distance or velocity in these combinations.
In summary, among the given options, only P = W / T provides the correct dimensional and conceptual form for the engine’s power under the stated conditions, while the others fail to match the definition of power or violate dimensional consistency.

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