Instantaneous Power from Force and Velocity
Instantaneous mechanical power delivered by a force is dW/dt=F dot v; the net power also equals dK/dt for a constant-mass particle.
Why this shows up in the exam
Time-dependent vector forces · Powered circular motion · Power at a specified instant
Learn the idea
Instantaneous power is the rate at which force transfers energy. A force does work fastest when it has a large component along a fast velocity, while a purely perpendicular force has zero instantaneous power.
🧠 Memory hook: Dot force with velocity for power now.
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 = F . v — instantaneous force power
- P_net = dK/dt — net power for particle motion
- P = Fv cos(theta) — magnitude-angle form
How to approach it
- 1Find velocity at the requested instant
- 2Evaluate the relevant force
- 3Take F dot v and check watts
Common slip-ups that cost marks
- •Using Fv without the angle
- •Confusing average and instantaneous power
- •Assigning centripetal force positive power at constant speed
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
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.
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.