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Dynamics of a particle moving in a straight line practice problems Edexcel IAL Mechanics 1, Chapter 3

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 structured exam question

Newton's laws, F = ma along a line, friction with F = μR, particles on inclined planes, lifts, and connected particles over pulleys. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page
  1. Key equations
  2. Warm-up questions
  3. Exam-style questions
  4. Exam question practice
  5. Common mistakes
  6. Keep going

Key equations for dynamics of a particle moving in a straight line

F = maresultant force = mass × acceleration
W = mgweight, with g = 9.8
F ≤ μRfriction; F = μR when moving or about to move
mg sin α, mg cos αweight resolved along and perpendicular to a plane at angle α

Take g = 9.8 m s−2, as the WME01 paper asks, and give answers to 2 or 3 significant figures. Answers within 2.5% are marked correct, so rounding along the way is fine. Revise the methods in our A level Maths mechanics guide.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up
A resultant force of 12 N acts on a particle of mass 3 kg. Find its acceleration.
m s−2

Hint

F = ma.

Worked solution
  1. 12 = 3a.
  2. a = 4 m s−2.
Q2Warm-up
Find the weight of a box of mass 5 kg.
N

Hint

W = mg with g = 9.8.

Worked solution
  1. W = 5 × 9.8 = 49 N.
Q3Warm-up
In a pulley question the string is modelled as light. What does this tell you?

Hint

Light and inextensible mean different things.

Worked solution
  1. Light means the mass of the string is ignored, so the tension is the same all along it.
  2. Inextensible is the one that means the particles share the same acceleration. The answer is B.

Exam-style questions

Questions at the level of the Edexcel IAL Mechanics 1 exam. The ones marked Challenge combine more than one idea.

Q4Exam-styleLifts
A woman of mass 60 kg stands in a lift that is accelerating upwards at 1.2 m s−2. Find the normal reaction from the floor of the lift on her.
N

Hint

Draw her forces: R up, 60g down. The resultant is upwards.

Worked solution
  1. Resolve upwards, F = ma: R − 60g = 60 × 1.2.
  2. R = 60 × 9.8 + 72 = 660 N.
Q5Exam-style
A box of mass 2 kg is pulled along a rough horizontal floor by a horizontal force of 15 N. The coefficient of friction is 0.4. Find the acceleration of the box.
m s−2

Hint

First find R by resolving vertically, then friction = μR because the box is moving.

Worked solution
  1. Vertically: R = 2g = 19.6 N, so friction F = 0.4 × 19.6 = 7.84 N.
  2. Horizontally: 15 − 7.84 = 2a.
  3. a = 3.58 m s−2.
Q6Exam-styleInclined plane
A particle slides down a rough plane inclined at 30° to the horizontal. The coefficient of friction is 0.2. Find its acceleration.
m s−2

Hint

Resolve perpendicular to the plane for R, then along the plane. Does the mass matter?

Worked solution
  1. Perpendicular: R = mg cos 30°. Friction acts up the plane: F = 0.2mg cos 30°.
  2. Along the plane: mg sin 30° − 0.2mg cos 30° = ma, and m cancels.
  3. a = 9.8(0.5 − 0.2 × 0.866) = 3.20 m s−2.
Q7Exam-styleConnected particles
Particle A of mass 3 kg lies on a smooth horizontal table. It is joined by a light inextensible string, passing over a smooth pulley at the edge of the table, to particle B of mass 2 kg hanging freely. The system is released from rest. Find the acceleration.
m s−2

Hint

Write F = ma for each particle separately, then add the equations to remove T.

Worked solution
  1. For A (horizontal): T = 3a. For B (downwards): 2g − T = 2a.
  2. Adding: 2g = 5a.
  3. a = 19.6/5 = 3.92 m s−2.
Q8ChallengePulleys
Particles of mass 5 kg and 3 kg hang on either side of a smooth fixed pulley, joined by a light inextensible string. The system is released from rest. Find the tension in the string.
N

Hint

Find the acceleration first, from the two equations of motion, then substitute back.

Worked solution
  1. 5 kg (down): 5g − T = 5a. 3 kg (up): T − 3g = 3a.
  2. Adding: 2g = 8a, so a = 2.45 m s−2.
  3. T = 3(9.8 + 2.45) = 36.8 N (3 s.f.).

Exam question practice

One original structured question in the style of the WME01 paper. Answer it in full, with working, before you open the mark scheme: M marks are for a correct method, A marks for accurate answers that follow from it, and B marks for a correct statement on its own.

Structured exam question style · 6 points · about 10 minutes

A box of mass 10 kg is pulled along rough horizontal ground by a rope inclined at 30° above the horizontal. The tension in the rope is 50 N and the coefficient of friction between the box and the ground is 0.3. The box is modelled as a particle.

  1. (a) Find the normal reaction between the box and the ground.
  2. (b) Find the acceleration of the box.
  3. (c) State how you have used the modelling assumption that the box is a particle.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

Vertically: R + 50 sin 30° = 10g, so R = 98 − 25 = 73 N.

Part (b)

Friction = 0.3 × 73 = 21.9 N. Horizontally: 50 cos 30° − 21.9 = 10a, so a = (43.30 − 21.9)/10 = 2.14 m s−2.

Part (c)

The box's size is ignored, so all the forces act at one point and the box does not rotate.

Your mark: 0 of 6

Common mistakes in dynamics of a particle moving in a straight line

Keep going

Revise the ideas behind these questions:

Then try real exam questions: Edexcel IAL Mechanics 1 past papers, with official scoring guidelines. · All Edexcel IAL Mechanics 1 units