Physics · Work, Energy And Power · NEET
No. Work (W) is the total energy transferred and its unit is the joule (J). Power (P) is how FAST that work is done, and its unit is the watt (W). Two crane motors can lift the same load (same work), but the faster one uses more power. Think: work = distance covered, power = speed. In NEET, a question that gives a TIME almost always wants power, not work.
Start from P = W/t. Work by a constant force is W = F·s (with force along motion). So P = F·s/t. But s/t is velocity v, giving P = F·v. Because both P = F·s and the dot product carry a cosine of the angle, the full form is P = F·v = Fv cos(theta), where theta is the angle between force and velocity. This form is used whenever a body moves at constant or known speed, like a lift or a vehicle.
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 magnitude only, no direction. It can be positive (force adds energy), negative (force removes energy, like friction), or zero (force perpendicular to velocity).
Average power = total work / total time (P_avg = W/t), the overall rate for the whole journey. Instantaneous power is the rate at a single instant, P_inst = F·v using the speed at that moment. If force or speed keeps changing (like a time-dependent force), you must use the instantaneous form. This split is the topic of the next page: average power vs instantaneous power.
1 horsepower (hp) = 746 W (about three-quarters of a kilowatt). 1 kilowatt (kW) = 1000 W. A kilowatt-hour (kWh) is a unit of ENERGY, not power: it is the energy used when 1 kW runs for 1 hour, so 1 kWh = 1000 W x 3600 s = 3.6 x 10^6 J. Do not confuse the kWh (energy) with the kW (power).
A body of mass 1 kg begins to move under the action of a time-dependent force F = (2t i + 3t^2 j) N, where i and j are unit vectors along the x and y axes. What power will be developed by the force at time t?
A particle moves with a velocity (6 i - 4 j + 3 k) m/s under the action of a constant force F = (10 i + 10 j + 20 k) N. The instantaneous power applied to the particle is
An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 m/s. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift (in watts) is (g = 10 m/s^2)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Power is the time rate at which work is done or energy is transferred. If work W is done in time t, then power P = W/t. It measures how fast energy is used, not the total amount.
The SI unit of power is the watt (W). One watt equals one joule per second (1 W = 1 J/s). Larger units are the kilowatt (1 kW = 1000 W) and horsepower (1 hp = 746 W).
The two main formulas are P = W/t (work over time) and P = F·v = Fv cos(theta) (force times velocity). Use P = W/t when you know work and time; use P = F·v when you know force and speed, such as for a lift or moving vehicle.
Power is a scalar quantity. It comes from the dot product of force and velocity, and a dot product always gives a scalar, so power has magnitude but no direction.
Power = work/time = (M L^2 T^-2) / T = M L^2 T^-3. So the dimensional formula of power is [M L^2 T^-3]. NEET sometimes tests this directly in unit-and-dimension questions.
