Mechanics is the part of WAEC Physics where method beats memory. Most questions give you a situation — a car braking, a ball dropped from a height, two trolleys colliding — and reward you for reading it correctly, choosing the right equation, and showing every step. If you can read a motion graph, draw the forces on a body, and decide whether a problem is about momentum or energy, you can answer most of the mechanics paper.
This guide covers the topics that come up most often: motion and graphs, forces and Newton’s laws, momentum and energy, moments, and circular motion. Work through the examples with a pen.
Key Takeaways
- On a velocity–time graph, the gradient gives acceleration and the area under the graph gives distance travelled.
- Find the resultant force first: unbalanced force, not the largest single force, causes acceleration.
- Momentum is conserved in a collision, but kinetic energy is only conserved when the collision is elastic.
The Mechanics Map: What WAEC Actually Tests
Mechanics questions fall into a small set of patterns. Learn to recognise the pattern before you reach for an equation, because the pattern tells you which quantity is conserved and which formula fits.
| Topic | Typical question |
|---|---|
| Motion and graphs | Acceleration or distance from a graph or description |
| Forces and Newton’s laws | Resultant force, acceleration, tension or friction |
| Momentum | Collisions, recoil, objects sticking together |
| Work, energy and power | Falling bodies, energy transfer, efficiency |
| Moments and equilibrium | Balanced beams and turning effects |
| Circular motion | Centripetal acceleration and force |
Before you start, ask what is moving, what acts on it, and what stays the same. A speeding car is a forces question, a collision is a momentum question, and a falling ball is usually an energy question.
Motion: Equations and Graphs
For motion with constant acceleration, three equations carry almost every calculation: v = u + at, s = ut + ½at², and v² = u² + 2as, where u is initial velocity, v is final velocity, a is acceleration, s is distance, and t is time. Choose the equation that contains what you know and what you are asked to find, without a quantity you do not know.
Worked example 1. A car starts from rest and accelerates uniformly at 2.5 m/s² for 8 s. Find its final velocity and the distance covered. Using v = u + at: v = 0 + (2.5 × 8) = 20 m/s. Using s = ut + ½at²: s = 0 + ½ × 2.5 × 8² = 80 m. Without the time, v² = u² + 2as would have been the right choice, because it has no t in it.
Graphs test the same ideas visually. On a distance–time graph, the gradient is velocity; on a velocity–time graph, the gradient is acceleration and the area under the graph is the distance travelled. Split a mixed velocity–time shape into a triangle and a rectangle, find each area, and add them.
Forces and Newton’s Laws
Newton’s first law says a body keeps moving at constant velocity unless a resultant force acts on it; his second gives the size of the effect, F = ma; his third says forces always come in equal, opposite pairs.
Before calculating, draw the forces: weight downwards (W = mg), friction opposing motion, tension along a string, and the normal reaction perpendicular to a surface. Resultant force equals the forces in the direction of motion minus those opposing it.
Worked example 2. A 4 kg block is pushed across a rough floor with a force of 20 N while friction opposes the motion with 8 N. Taking g = 10 m/s², find the acceleration and the weight of the block. Resultant force = 20 − 8 = 12 N. Acceleration = F / m = 12 / 4 = 3 m/s². Weight = mg = 4 × 10 = 40 N. The common mistake is to use 20 N as the resultant force and ignore friction.
Momentum and Energy: Two Ideas Students Confuse
Momentum and energy are both conserved in the right conditions, but they are not the same thing, and examiners set questions that separate them. Momentum, p = mv, is a vector, so direction matters. In a collision with no external force, total momentum before impact equals total momentum after it. Energy, by contrast, changes form: a falling body loses potential energy and gains kinetic energy.
Worked example 3: momentum. A 2 kg trolley moving at 3 m/s collides with a stationary 3 kg trolley and the two move off together. Total momentum before = (2 × 3) + (3 × 0) = 6 kg m/s. After impact the combined mass is 5 kg, so 6 = 5 × v, giving v = 1.2 m/s. Kinetic energy, however, is not conserved here: before it was ½ × 2 × 3² = 9 J, and after it is ½ × 5 × 1.2² = 3.6 J. The missing energy went into sound, heat and deformation. That is what makes the collision inelastic, and naming it correctly can earn a mark on its own.
Worked example 4: energy. A 0.5 kg ball is dropped from a height of 20 m. Ignoring air resistance and taking g = 10 m/s², find its speed just before it hits the ground. Gravitational potential energy lost = mgh = 0.5 × 10 × 20 = 100 J. This becomes kinetic energy, so 100 = ½ × 0.5 × v², giving v² = 400 and v = 20 m/s. The same answer follows from v² = u² + 2gh, a useful check.
Moments and Circular Motion, in Brief
A moment is a turning effect: force multiplied by the perpendicular distance from the pivot. A see-saw balances when clockwise moments equal anticlockwise moments, so a 60 N child at 2 m (120 Nm) is balanced by a 40 N child at 3 m (also 120 Nm).
Circular motion needs a force towards the centre, called the centripetal force, and produces centripetal acceleration a = v² / r. A car at 20 m/s around a bend of radius 50 m has a centripetal acceleration of 20² / 50 = 8 m/s². Its direction is always towards the centre, even at constant speed, because velocity is a vector and its direction keeps changing.
How Marks Are Won and Lost in Theory Answers
WAEC theory marking rewards a visible method: state the principle, write the equation, substitute with units, and give the final answer with its unit. A bare number with no working can lose every method mark if it is wrong, while a well-set-out solution with an arithmetic slip can still earn most of them.
Common Mistakes to Avoid
- Using speed when the question needs velocity, or forgetting that a change of direction alone changes velocity.
- Treating the applied force as the resultant force and ignoring friction, weight or tension.
- Assuming kinetic energy is conserved in every collision. Only momentum is conserved in all collisions.
- Mixing up distance and displacement on graphs, especially when a body returns to its starting point.
- Dropping units, or giving an answer in centimetres when the equation needs metres.
- Memorising worked examples instead of practising new numbers. Examiners change the numbers; they rarely change the pattern.
A Four-Week Mechanics Revision Plan
Week 1: Motion and graphs. Relearn the three equations of motion and practise graph reading until gradient and area are automatic.
Week 2: Forces. Practise free-body diagrams and resultant-force calculations, including friction and tension.
Week 3: Momentum and energy. Work collision and falling-body problems side by side, and write one line in each solution saying what is conserved and why.
Week 4: Mixed papers and weak spots. Sit full mechanics sections under timed conditions, mark them honestly, and revise only what you actually got wrong. Pair this plan with the WAEC Physics Practical Guide, since the practical paper tests the same ideas with apparatus, and test yourself in the timed practice area on this site. For the current 2027 window, check the exam hub: the May/June window there is still proposed, not a final WAEC timetable.
Frequently Asked Questions
Do I need to memorise every WAEC Physics equation?
Build a personal formula sheet while you revise and practise the core mechanics equations until they are automatic, rather than meeting them for the first time in the examination hall.
What is the difference between speed and velocity?
Speed is a scalar with magnitude only; velocity is a vector with magnitude and direction. A car on a roundabout at a steady 20 m/s has constant speed but changing velocity, because its direction keeps changing.
How do I answer a question that mixes two topics?
Split it into stages and use the output of one stage as the input of the next. A ball may fall (energy), then collide (momentum), then slide to rest (friction). Identify each stage, write its equation, and carry the numbers forward.