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

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).

类似问题

A car of mass 615.2 kg is driven along a straight flat road by an engine that provides a constant driving force. The car engine does 2.3 kJ of work while travelling at a constant speed 13.2 m/s over a time period of 3.3 seconds. What was the power developed by the car engine?

How many, if any, factors are necessary to determine power? 1.) Force exerted. 2.) Distance the force moves. 3.) Time required to do the work.

A child pulls on a wagon with a force of 10 N. If the wagon moves a total of 50 m in 5 s, what is the average power generated by the child, in watts?

A child pulls on a wagon with a force of 75 N. If the wagon moves a total of 42 m in 3 min, what is the average power generated by the child, in watts?

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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