This unit is ≈17% of the A-Level Physics, across 7 lessons. Full syllabus
Lesson 3 of 7 · Mechanics and materials
Newton’s laws, drag and terminal velocity
8 min read · about 1 h 40 min with practice3 quick checks≈2% of the testCore: Core: tested on most papers
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Almost every force question on the mechanics paper comes down to one move: draw the forces on one body, find the resultant, and apply F=ma. Examiners test this with one-mark MCQs on Newton’s third-law pairs, 3–5 mark calculations on lifts, slopes and connected bodies, and 6-mark explanations of terminal velocity. None of it is hard once the method is fixed. Top candidates simply never skip the free-body diagram.
By the end you’ll be able to
State and apply Newton’s three laws, identifying Newton’s third-law force pairs correctly
Solve F = ma problems for connected bodies, lifts, inclined planes and towing
Explain how drag depends on speed and how a falling object reaches terminal velocity, with velocity–time graphs
Analyse motion with friction and describe factors affecting stopping and braking distances
Distinguish mass from weight and use W = mg in varying gravitational field strengths
What the exam asks
State a law (1–2 marks). The precise wording matters, especially for the third law.
Identify force pairs (MCQ). The favourite trap: weight and normal contact force are not a third-law pair.
Resultant force calculations: vehicles with driving and resistive forces, lifts, inclined planes, towing and pulleys.
Terminal velocity: explain the motion in terms of changing forces, sketch or interpret the v–t graph, and handle the parachute-opening stage. Often a 6-mark extended response.
Drag, friction and lift, qualitatively, and the factors affecting stopping distance.
Mass and weight, W=mg, including other planets.
Core ideas
The three laws
Law
Statement
How the exam uses it
First
An object stays at rest or moves with constant velocity unless a resultant force acts on it.
Constant velocity ⇒ resultant force is zero (forces balance).
Second
The rate of change of momentum of an object is proportional to the resultant force on it, and takes place in the direction of that force. For constant mass, .
vii.Check your understanding
3 questions on Newton’s laws, drag and terminal velocity. Every option is explained once you answer.
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PromptCard 1 of 3
State Newton’s first law.
F=ma
Resultant force ⇒ acceleration in the same direction as the resultant.
Third
If body A exerts a force on body B, then B exerts a force on A that is equal in magnitude and opposite in direction.
Pairs act on different bodies, so they never cancel.
A third-law pair is always: the same type of force (both gravitational, both contact, both electrostatic), equal in size, opposite in direction, acting on two different bodies, along the same line.
Mass and weight
Mass (kg) measures the amount of matter and inertia, and it is the same everywhere. Weight is the gravitational force on the mass, W=mg, in newtons, where g is the gravitational field strength (9.81N kg−1 on Earth, about 1.6N kg−1 on the Moon). Weight acts at the centre of mass.
The F=ma recipe
Isolate one body and draw only the forces acting on it.
Choose the positive direction to be the direction of acceleration.
Write resultant force = (forces in the + direction) − (forces against it) =ma.
For connected bodies, find a from the whole system (the tension is internal, so it cancels), then isolate one body to find the tension.
Lifts (up positive, R = floor or scale reading):
Motion of lift
Acceleration
Reading R
speeding up going up, or slowing down going down
upwards
R=m(g+a)>mg
constant velocity (either way) or at rest
zero
R=mg
slowing down going up, or speeding up going down
downwards
R=m(g−a)<mg
free fall (cable snaps)
g downwards
R=0 (“weightless”)
Slopes at angle θ: resolve the weight into mgsinθdown the slope and mgcosθinto the slope. With no other perpendicular forces, the normal contact force is mgcosθ.
Friction, drag and lift
Friction acts parallel to the surfaces in contact and opposes relative motion (or the tendency to move). Work done against it becomes internal (thermal) energy.
Drag is the resistive force on an object moving through a fluid. It acts opposite to the velocity and increases with speed. It also depends on cross-sectional area, shape and the fluid’s density and viscosity. For fast objects in air, drag is roughly proportional to v2.
Lift is a force perpendicular to the fluid flow, produced when a wing or aerofoil deflects air downwards. By Newton’s third law, the air pushes the wing up.
Terminal velocity: the chain of reasoning
At release, only the weight acts, so a=g.
As speed increases, drag increases, so the resultant force (W−D) decreases and the acceleration decreases. The v–t graph gets less steep.
When drag equals weight (in a liquid, W=D+U including upthrust), the resultant force is zero, the acceleration is zero, and the velocity is constant. This is terminal velocity.
Parachute opens: the area increases, so drag suddenly exceeds weight. The resultant force is upwards and the skydiver decelerates, still moving down. As speed falls, drag falls, the deceleration decreases, and a new, lower terminal velocity is reached when drag equals weight again.
The same argument explains a car’s top speed: the driving force is fixed at maximum power, and resistive forces grow with speed until they equal it.
Thinking distance = speed × reaction time, so it is proportional to v. It increases with tiredness, alcohol, drugs and distraction.
Braking distance = 2av2, so it is proportional to v2 for a given deceleration. It increases with wet or icy roads, worn tyres or brakes, and extra mass.
Worked examples
Exam technique
Free-body diagram first, always. One labelled arrow per force, drawn from the point where it acts. It earns marks in “draw” questions and stops you inventing a “force of motion”.
For third-law MCQs, say the pair aloud: “Earth pulls book, book pulls Earth”. If the second force doesn’t swap the two bodies, it isn’t the pair.
Connected bodies: system first for a, then one body for the tension. Check with the other body.
“Explain” terminal velocity questions need a chain: speed ↑ ⇒ drag ↑ ⇒ resultant ↓ ⇒ acceleration ↓ ⇒ constant velocity when forces balance. Every link is a creditworthy step. Always say “resultant force”, never just “force”.
Stopping-distance data: thinking distances scale with v, braking distances with v2. Doubling speed quadruples braking distance.
Common mistakes
Quick recap
First law: zero resultant force ⇔ constant velocity (including at rest).
Second law: resultant force = rate of change of momentum; F=ma for constant mass; acceleration is in the direction of the resultant.
Third-law pairs: same type, equal, opposite, on different bodies.
Lifts: R=m(g+a) when the acceleration is up, and m(g−a) when it is down.
Slopes: mgsinθ along the slope, mgcosθ into it.
Terminal velocity: drag rises with speed until drag (+ upthrust) = weight, giving a=0.