Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.
Why this shows up in the exam
You need to solve problems involving instantaneous and average power in NEET.
How NEET tests this
Learn the idea
Power is the rate at which work is done or energy is transferred; the instant‑aneous value is given by P = F·v when force and velocity are along the same line.
🧠 Memory hook: Power = Force × Speed – like a car: more push (force) or faster drive (speed) gives higher power.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = dW/dt (SI unit watt = N·m s⁻¹)
- Instantaneous power P = F·v (dot product)
- Average power = total work ÷ total time
- If force is constant, P is constant only when velocity is constant
- Velocity v = dx/dt for a particle moving along a line
How to approach it
- 1Write the given displacement x(t) and differentiate to obtain velocity v(t)
- 2Identify the magnitude and direction of the force; if it is along the motion use P = F·v
- 3Substitute the numerical values at the required instant (or use the constant values)
- 4Compute P in watts
Worked example — watch it click
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):
- A)7
- B)6
- ✅10
- D)5
The concept behind this problem
The example checks that you can turn the given displacement into velocity by differentiation and then apply the fundamental relation P = F·v.
Step by step
- 1Given displacement x = 2t - 1, velocity v = dx/dt = 2 m/s (constant).
- 2Instantaneous power P = F·v = 5 N × 2 m/s = 10 W.
- 3The power is constant since both force and velocity are constant.
Watch out
Students often plug the displacement directly into P = F·v instead of first finding the velocity.
Common slip-ups that cost marks
- •Treating displacement as velocity – always differentiate first
- •Using average‑power formula when the question asks for instantaneous power
- •Ignoring the sign/direction of force; remember P = F·v is a scalar product
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
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):
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Work by a Constant Force
For a constant force, work is the scalar product of force and displacement, so its sign is set by the angle between those vectors and not by force magnitude alone.