Constant-Power Motion
For one-dimensional constant-mass motion under constant net power, P=mv(dv/dt), giving v^2=v_0^2+2Pt/m and displacement from integrating that speed.
Why this shows up in the exam
Constant-power engines · Time scaling of speed · Distance-time power laws
Learn the idea
Constant power produces acceleration that falls as speed rises. When a machine supplies fixed power, the same energy arrives each second, so speed grows like square root of time rather than linearly.
🧠 Memory hook: Fixed power adds equal kinetic energy each second.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = mv dv/dt — constant-mass one-dimensional power
- v² = v₀²+2Pt/m — speed under constant net power
- x-x₀ = integral v dt — displacement after finding speed
How to approach it
- 1Write dK/dt=P
- 2Integrate for v(t)
- 3Integrate again only if displacement is asked
Common slip-ups that cost marks
- •Assuming constant power means constant force
- •Using v proportional to t
- •Forgetting nonzero initial 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.