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?

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BlackTom AI · Accepted Answer

To determine engine power, start from the basic definition: power is the rate at which work is done, so P = work done over time.
Option a: P = W/T. This is the standard and correct expression for average power when W is the work done (in joules or kilojoules) and T is the time in seconds. It directly embodies the definition of power as energy per unit time.
Option b: P = W*T/D. Here, rearranging the known relation D = V*T (constant speed) gives T/D = 1/V, so this would yield P = W*(1/V). This does not correspond to energy per unit time unless V happens to equal W, which is generally false. Moreover, the units would be J*s/m, not J/s, so this is not a correct expression for power.
Option c: P = W*D/T. Since D/T = V (because D = V*T), this becomes P = W*V. But mixing energy (W) with velocity (V) yields units J*(m/s) which is not J/s; thus this form does not represent power. Therefore it is incorrect.
Option d: P = W*V/D. Using D = V*T, we can rewrite D in terms of V and T, giving D = V*T and thus P = W*V/(V*T) = W/T. This matches the definition of power, so this expression is valid as another form for the same quantity. When W is in kilojoules and T in seconds, P will be in kilowatts (after proper unit conversion), consistent with P = W/T.
In summary, option a is the direct, correct expression for power. Options b and c fail due to dimensional inconsistency or incorrect relationship to power, while option d is algebraically equivalent to option a under the given condition D = V*T and therefore also valid (with appropriate units).

MUF0121 Physics Unit 1 - Semester 2, 2025 6.13 Power

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