Instantaneous Power

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A car moves along a straight highway at a steady speed of 20 m/s while its engine works against a total resistive force of 1800 N. What power must the engine deliver to maintain this constant speed?

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Instantaneous power delivered by a force equals the dot product of force and velocity, $P = \vec{F}\cdot\vec{v}$, which for motion in the direction of the force reduces to $P = Fv$. At constant speed the engine's driving force exactly balances the resistive force, so the engine must supply power equal to the resistive force times the speed. Multiplying gives $P = 1800 	imes 20 = 36000	ext{ W} = 36	ext{ kW}$. The option 18 kW halves the result, perhaps mistakenly inserting a one-half factor that belongs to kinetic energy, not power. The option 90 kW divides force by speed incorrectly. The option 3.6 kW misplaces a decimal by a factor of ten. Note that no net work is done on the car as a whole, since its kinetic energy stays constant; the engine's entire output is dissipated against road resistance and air drag. This is precisely why fuel consumption climbs steeply at higher cruising speeds, because the power demanded by a fixed resistive force grows in direct proportion to velocity. This applies the NCERT relation between instantaneous power, force, and velocity. As a unit check, newtons times metres per second equals watts, and tens of kilowatts is a realistic engine output for highway cruising.

Instantaneous Power

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