5 high-yield, syllabus-aligned questions on Mechanics, covering 14 individually creditable mark points. Each one shows the answer that scores full marks under our guide, which phrase earns which mark, and a common incomplete answer — so you can see the difference rather than guess at it.
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Every question and solution is reviewed by examiners versed in WAEC and JAMB, each with more than thirty years of experience.
Mark allocations are TopMarks’ own, written against the published syllabus and Chief Examiners’ reports. They are a guide to how these answers are usually credited, not an official marking scheme.
Define3 marks
Define work, energy and power, and state the SI unit of each.
TopMarks model answer
Work is the product of the force applied and the distance moved in the direction of the force; its SI unit is the joule, J. Energy is the capacity to do work; its SI unit is also the joule. Power is the rate of doing work, that is the work done per unit time; its SI unit is the watt, W.
Suggested marking guide
1Work defined with its unit
2Energy defined
3Power defined with its unit
Why it scores
Every one of the three marks includes the UNIT. Definitions in Physics are routinely asked with “and state its unit” attached, and the unit is never a free extra — it is part of the mark. Note also the phrase “in the direction of the force”: work done by a force perpendicular to the motion is zero, which is why that clause has to be there.
A common incomplete answer
“Work is force times distance measured in joules, and power is the rate of doing work.”
What it costs: Two marks of three. Work is fully defined with its unit. Energy is never defined at all, and power is given without the watt.
Key ideas to include: force, distance in the direction of the force, joule, capacity to do work, rate, watt.
State3 marks
State Newton's three laws of motion.
TopMarks model answer
First law: a body continues in its state of rest, or of uniform motion in a straight line, unless it is acted upon by an external force. Second law: the rate of change of momentum of a body is directly proportional to the applied force, and the change takes place in the direction of the force. Third law: to every action there is an equal and opposite reaction.
Suggested marking guide
1First law with the condition
2Second law in terms of rate of change of momentum
3Third law
Why it scores
The second law is the one that costs marks. F = ma is a CONSEQUENCE of the second law for a constant mass, not the law itself. WAEC wants the momentum statement — “the rate of change of momentum is directly proportional to the applied force” — and gives no credit for the formula alone.
A common incomplete answer
“A body stays at rest unless a force acts on it. Force equals mass times acceleration. Action and reaction are equal and opposite.”
What it costs: One mark of three. The first and third laws are credited. The second is given as a formula rather than as the law, so it does not score.
Key ideas to include: inertia, external force, rate of change of momentum, action, reaction.
Calculate3 marks
A body of mass 5 kg moving at 12 m s⁻¹ is brought to rest in 4 s. Calculate the retarding force acting on it.
TopMarks model answer
Acceleration a = (v - u) ÷ t = (0 - 12) ÷ 4 = -3 m s⁻². Force F = ma = 5 x (-3) = -15 N. The magnitude of the retarding force is 15 N, the negative sign showing that it acts against the direction of motion.
Suggested marking guide
1Acceleration calculated correctly
2Newton’s second law applied
3Correct answer with the unit
The working, line by line
1a = (v - u) ÷ t = (0 - 12) ÷ 4 = -3 m s⁻² — The body is brought TO REST, so the final velocity v is 0 and the initial velocity u is 12. Getting these the wrong way round is the commonest error in the question.
2F = ma = 5 x (-3) = -15 N — Write the formula before substituting — it is a separate mark from the arithmetic.
3Retarding force = 15 N — State the magnitude and explain the minus sign rather than quietly dropping it.
Why it scores
A force question with a time in it is almost always asking for the acceleration first. Going straight from mass and velocity to a “force” is dimensionally wrong — 5 x 12 gives momentum in kg m s⁻¹, not force in newtons — and the answer will be numerically wrong too.
A common incomplete answer
“F = ma = 5 x 12 = 60 N”
What it costs: Two marks of three. The formula is credited, but 12 is a velocity, not an acceleration. The acceleration step is skipped, so both the intermediate mark and the answer mark fall.
Key ideas to include: initial velocity, final velocity, acceleration, retardation, newton.
State3 marks
State the principle of conservation of linear momentum and give one application of it.
TopMarks model answer
The principle of conservation of linear momentum states that when two or more bodies interact, the total momentum of the system before the interaction is equal to the total momentum after the interaction, provided that no external force acts on the system. An application is the recoil of a gun: the forward momentum of the bullet is equal and opposite to the backward momentum of the gun. The principle also explains the motion of a rocket, which is driven forward by the momentum of the exhaust gases expelled backwards.
Suggested marking guide
1Total momentum before equals total momentum after
2The condition that no external force acts
3A valid application
Why it scores
The condition is a mark, and it is the mark almost nobody gives. Momentum is only conserved in a system on which no NET EXTERNAL force acts — which is why a rolling ball eventually stops, and why the principle still holds if you include the earth in the system. State the condition every time.
A common incomplete answer
“The momentum before a collision is equal to the momentum after the collision.”
What it costs: One mark of three. The statement is credited and the word “collision” just carries the application mark, but the condition — that no external force acts — is missing, and that is the clause that makes the principle true.
Key ideas to include: linear momentum, total momentum, external force, recoil, isolated system.
Explain2 marks
Explain why a passenger in a moving vehicle lurches forward when the vehicle stops suddenly.
TopMarks model answer
By Newton's first law, the passenger's body tends to continue moving forward in a straight line with the velocity it already had, because of its inertia. The braking force acts on the vehicle and on the parts of the body in contact with it, but not directly on the upper body, so the upper body continues forward while the lower body is stopped with the vehicle, and the passenger lurches forward.
Suggested marking guide
1Inertia or the first law named
2The body continues in motion while the vehicle stops
Why it scores
Two marks: one for the PRINCIPLE, one for the APPLICATION of it to this situation. The word “inertia” by itself is a label; the mark comes from saying what the inertia causes the body to do. This pattern — name the law, then apply it — earns the marks in every “explain the everyday situation” question in Mechanics.
A common incomplete answer
“Because the body keeps moving forward when the bus stops.”
What it costs: One mark of two. The observation is correct and credited, but neither inertia nor Newton’s first law is named, so the physics behind it is never given.
Key ideas to include: inertia, Newton's first law, uniform motion, braking force.
Practise Mechanics on real questions
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