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At any instant of time t, the displacement of any particle is given by 2t − 1 (SI unit) under the influence of force of 5 N. The value of instantaneous power is (in SI unit):
v = dx/dt = d(2t - 1)/dt = 2 m/s -> Instantaneous Power P = F × v = 5 × 2 = 10 W!
The velocity v of the particle is the first time derivative of its position function x(t) = 2t - 1:
Instantaneous power P delivered by a force F to a particle moving with velocity v in the same direction is:
Substituting F = 5 N and v = 2 m/s:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Adds force and velocity (5 + 2 = 7) instead of multiplying.
Arbitrary calculation error.
Exact product: P = F × v = 5 × 2 = 10 SI units.
Assumes velocity is 1 m/s.
Students search for a value of t to plug into 2t - 1, getting confused because velocity is constant.
"Instantaneous power is the rate of doing work, given by the dot product of force and instantaneous velocity: P = F · v."
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