Master every formula — W = Fd, P = W/t, KE = ½mv², and GPE = mgh — with clear explanations, real-life examples, and fully solved exam problems.
In everyday life, "work" means any effort you make. In physics, the definition is much more precise: work is done when a force moves an object in the direction of that force. Both conditions must exist — a force and movement in the direction of that force. If either one is missing, the physics definition of work is zero, even if you feel exhausted.
A classic example that confuses students: you hold a heavy bag of groceries perfectly still for ten minutes. You feel tired, but you do zero joules of work on the bag because the bag does not move. Your muscles do internal work, but no work is done on the object itself.
W = F × d
One Joule equals one Newton-metre (1 J = 1 N·m). You do exactly 1 J of work when you push an object with 1 N of force across 1 m.
The force and the movement must point in the same direction for maximum work. When you carry a bag horizontally, gravity pulls it straight down — perpendicular to your horizontal movement. Gravity therefore does no work on the bag as you walk forward. Only the horizontal component of any force contributes to work done horizontally. O-Level mark schemes regularly test this distinction, so keep it in mind.
Power measures how quickly work is done. Two people might do the same amount of work climbing a flight of stairs, but the person who reaches the top faster uses greater power. Power does not tell you how much work is done — it tells you the rate at which that work happens.
P = W ÷ t
One Watt equals one Joule per second (1 W = 1 J/s). A 60 W light bulb transfers 60 J of electrical energy every second.
Energy is the ability to do work. An object or system that has energy can exert a force and cause movement. Energy comes in many forms — kinetic, gravitational potential, chemical, thermal, electrical, and more — but you can always convert it from one form to another. The total amount of energy in a closed system never changes; this is the Law of Conservation of Energy.
All forms of energy are measured in Joules (J), the same unit as work. This is not a coincidence — doing work on an object transfers energy to it.
Kinetic energy is the energy an object possesses because of its motion. Any moving object — a car, a falling raindrop, a flying cricket ball — carries kinetic energy. The faster it moves or the more massive it is, the more kinetic energy it holds.
KE = ½ × m × v²
Because velocity appears squared in the formula, even a small increase in speed produces a large increase in kinetic energy. If you double an object's speed, its kinetic energy becomes four times larger (2² = 4). If you triple the speed, kinetic energy becomes nine times larger (3² = 9).
This is why motorway speed limits have such a dramatic effect on crash severity. A car travelling at 60 mph carries four times the kinetic energy of one travelling at 30 mph — and therefore causes far greater damage in a collision.
Always square the velocity before multiplying by the mass. Students who multiply ½ × m first and then multiply by v (forgetting the square) get a completely wrong answer. Write out every step: calculate v² first, then multiply by ½ × m.
Gravitational potential energy is the energy stored in an object because of its height above a reference point (usually the ground). When you lift an object, you do work against gravity and transfer energy into the object as GPE. When the object falls, that stored GPE converts back into kinetic energy.
GPE = m × g × h
A classic exam scenario involves a falling object. At maximum height, the object holds maximum GPE and zero KE (it is momentarily stationary). As it falls, GPE decreases and KE increases by exactly the same amount — assuming no air resistance. At the moment just before impact, all the GPE has converted into KE.
You can use this relationship to find the speed at any height: set GPE lost = KE gained, then solve for v.
Energy cannot be created or destroyed — it only transfers from one form to another. This principle underlies every energy calculation in physics. In a real system, some energy always converts into thermal energy (heat) through friction or air resistance. This energy is not lost; it simply becomes less useful.
Exam questions sometimes ask you to calculate the energy "wasted" or "lost to heat." Use this approach: Energy wasted = Total input energy − Useful output energy.
Read through every step carefully. In an exam, write out each line exactly like this — examiners award marks for working, not just the final number.
Question: A person pushes a box with a force of 25 N across a distance of 8 m. Calculate the work done.
Given: F = 25 N, d = 8 m
Formula: W = F × d
Substitution: W = 25 × 8
Answer: W = 200 J
Question: A motor does 4 500 J of work in 15 seconds. Calculate its power output.
Given: W = 4 500 J, t = 15 s
Formula: P = W ÷ t
Substitution: P = 4 500 ÷ 15
Answer: P = 300 W
Question: A 500 W pump does 15 000 J of work. How long does it take?
Given: P = 500 W, W = 15 000 J
Formula: t = W ÷ P
Substitution: t = 15 000 ÷ 500
Answer: t = 30 s
Question: A car of mass 1 200 kg travels at 20 m/s. Calculate its kinetic energy.
Given: m = 1 200 kg, v = 20 m/s
Formula: KE = ½ × m × v²
Step 1 — Square the velocity: v² = 20² = 400 m²/s²
Step 2 — Multiply: KE = ½ × 1 200 × 400 = 600 × 400
Answer: KE = 240 000 J (240 kJ)
Question: A 3 kg book sits on a shelf 2 m above the floor. Calculate its gravitational potential energy.
Given: m = 3 kg, g = 10 N/kg, h = 2 m
Formula: GPE = m × g × h
Substitution: GPE = 3 × 10 × 2
Answer: GPE = 60 J
Question: A 0.5 kg ball drops from a height of 5 m. Assuming no air resistance, calculate its speed just before it hits the ground.
Step 1 — Calculate GPE at the top:
GPE = m × g × h = 0.5 × 10 × 5 = 25 J
Step 2 — Set GPE lost equal to KE gained:
KE = 25 J
Step 3 — Solve for v:
½ × m × v² = 25
½ × 0.5 × v² = 25
0.25 × v² = 25
v² = 25 ÷ 0.25 = 100
Answer: v = √100 = 10 m/s
Question: A crane does 18 000 J of work lifting a load through 12 m. Calculate the force the crane applies.
Given: W = 18 000 J, d = 12 m
Formula: F = W ÷ d
Substitution: F = 18 000 ÷ 12
Answer: F = 1 500 N
Students regularly mix up these three concepts in exam answers. The distinction is straightforward once you fix the definitions in your memory:
A useful analogy: imagine filling a tank with water. Energy is the amount of water in the tank. Work is the act of pouring water in. Power is how fast you pour. All three are connected, but they describe different aspects of the same process.
Work, power, and energy connect through a single idea: forces transfer energy, and power tells you how fast that transfer happens. Once you see all three as parts of the same story, exam questions become far more predictable — and far easier to solve.