Short on time? This page is the recap. For explanations, graphs and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Choose the system first. Energy can cross its boundary (work by outside forces) or change form inside it (for example, friction turning kinetic energy into internal energy).
- Power is the rate of that transfer or conversion. Energy says how much; power says how fast.
- Average power uses the total energy change over the whole interval.
- Instantaneous power of a constant force depends on the speed at that instant, so it changes if the speed changes.
- A force at right angles to the velocity has zero power. A force against the velocity has negative power: it takes energy out.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| P_avg = ΔE / Δt | W = J/s | find average power from an energy change |
| P_avg = W / Δt | W is work in J | find average power from the work done by a force |
| P = F∥v = Fv cos θ | θ between F and v | find instantaneous power of a constant force |
| slope of E–t graph | W | power (flat = zero power) |
| area under P–t graph | J | energy transferred (below axis = energy out) |
| v_max = P_max / F_resistive | m/s | top speed at constant velocity on level ground |
| 1 kWh = 3.6 × 10⁶ J | energy, not power | convert electricity-bill energy to joules |
Assumptions behind the numbers
- The force is constant when you use P = F∥v. If the force changes, use total energy ÷ total time for the average power.
- Objects are treated as point objects; rotation is ignored.
- Near Earth’s surface, g = 9.8 m/s². Air resistance is ignored unless the question gives a resistive force.
- “Constant speed” means the net force is zero, so a driving force equals the forces it balances.
Mistakes to avoid
- Mixing up energy and power. Check units: J for energy, W for power.
- Using the whole force in P = Fv. Multiply by cos θ, the angle between force and velocity.
- Assuming constant force gives constant power. P rises as v rises.
- Forgetting the sign. Friction on a sliding object has negative power.
- Taking the mean of the start and end power when the power does not change at a steady rate. Use total energy ÷ total time.
- Minutes and hours left unconverted. Change time to seconds before dividing.
- Saying no power is involved at constant speed. Energy can flow in and out at equal rates.
Quick self-check
- A 1.2 kW motor runs for 5.0 min. How much energy does it deliver? (3.6 × 10⁵ J)
- A 200 N force acts at 60° to the velocity of a cart moving at 3.0 m/s. What is its power? (300 W)
- How many joules are in 1 kWh? (3.6 × 10⁶ J)
Next: practice questions.