Physics · Work, Energy And Power · NEET
Average power looks at the whole journey: P_avg = total work done / total time taken = W / t. Instantaneous power looks at one single instant: P = dW/dt = F . v. If a body's force or speed keeps changing, its instantaneous power changes moment to moment, but its average power is one single number for the full interval. Example: a car speeding up has rising instantaneous power, yet one fixed average power for the trip.
Work done in a tiny time is dW = F . dr (force dotted with small displacement). Power is the rate, so P = dW/dt = F . (dr/dt) = F . v, because dr/dt is velocity. The dot product appears because only the part of the force along the velocity does work. So P = Fv cos(theta), where theta is the angle between force and velocity.
Use the dot product component by component: if F = (Fx i + Fy j + Fz k) and v = (vx i + vy j + vz k), then P = F . v = Fx*vx + Fy*vy + Fz*vz. Multiply matching components, then add them (watch the signs). The answer is a single number in watts, because power is a scalar.
Power is a scalar. Even though it comes from the dot product of two vectors (force and velocity), a dot product always gives a scalar. So power has only a magnitude and a sign (positive when force helps motion, negative when it opposes), but no direction. Its SI unit is the watt (W) and dimensions are [M L^2 T^-3].
They are equal only when the power stays constant over the whole time interval, for example a motor lifting a load at steady speed against a constant force. If either the force or the speed changes with time (accelerating body, time-dependent force), the instantaneous power varies and will differ from the single average value. This is a favourite NEET trap.
A particle moves with a velocity (6i - 4j + 3k) m/s under the action of a constant force F = (10i + 10j + 20k) N. The instantaneous power applied to the particle is
At any instant of time t, the displacement of a particle is given by x = 2t - 1 (SI units), under the influence of a force of 5 N. The value of the instantaneous power is (in SI units)
A body of mass 1 kg begins to move under the action of a time-dependent force F = (2t i + 3t^2 j) N. What power will be developed by the force at time t?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Average power = total work done divided by total time: P_avg = W / t. It can also be written as P_avg = F . (average velocity) when force is constant. Its SI unit is the watt (W).
Instantaneous power is P = dW/dt = F . v = Fv cos(theta), where F is the force, v is the instantaneous velocity, and theta is the angle between them. It gives the rate of doing work at that exact instant.
If theta = 0 (force along motion), power is maximum and positive. If theta = 90 degrees, cos 90 = 0, so power is zero (like centripetal force in circular motion). If theta = 180 degrees, power is negative, meaning the force removes energy, like friction.
Yes. When the force opposes the velocity (angle greater than 90 degrees), P = Fv cos(theta) becomes negative. This means the force is taking energy out of the body, for example friction or a braking force slowing a car.
The SI unit of power is the watt (W), where 1 W = 1 joule per second (1 J/s). The dimensional formula of power is [M L^2 T^-3]. 1 horsepower (hp) = 746 W.
