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Vectors in mechanics practice problems Edexcel IAL Mechanics 1, Chapter 7

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

Vectors in i, j form: magnitude and direction, bearings, resultant forces, F = ma with vectors, and position and velocity with r = r0 + vt. 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 vectors in mechanics

|ai + bj| = √(a2 + b2)magnitude
tan θ = b/aangle with i
r = r0 + vtposition with constant velocity
v = u + atconstant acceleration, in vector form
F = mawith vectors

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
Find the speed of a particle moving with velocity (5i + 12j) m s−1.
m s−1

Hint

Speed is the magnitude of the velocity.

Worked solution
  1. Speed = √(52 + 122) = √169.
  2. = 13 m s−1.
Q2Warm-up
Find the angle between the vector (3i + 4j) and the unit vector i, in degrees.
°

Hint

Sketch it: the j part is opposite the angle.

Worked solution
  1. tan θ = 4/3.
  2. θ = 53.1° (3 s.f.).
Q3Warm-up
Two forces (2i + 3j) N and (4i − 7j) N act on a particle. Find the magnitude of the resultant force.
N

Hint

Add the i parts and the j parts.

Worked solution
  1. Resultant = (6i − 4j) N.
  2. Magnitude = √(36 + 16) = √52 = 7.21 N (3 s.f.).

Exam-style questions

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

Q4Exam-style
Forces (4i + 2j) N and (2i + 6j) N act on a particle of mass 2 kg. Find the magnitude of its acceleration.
m s−2

Hint

Find the resultant force, then use F = ma.

Worked solution
  1. Resultant = (6i + 8j) N, with magnitude √(36 + 64) = 10 N.
  2. a = 10/2 = 5 m s−2.
Q5Exam-style
A boat moves with velocity (−3i + 3j) km h−1, where i points east and j points north. On what bearing is it moving?

Hint

West 3 and north 3: sketch it, then measure clockwise from north.

Worked solution
  1. The boat moves north-west, at 45° between west and north.
  2. Clockwise from north, that is 360° − 45° = 315°: D.
Q6Exam-style
A particle starts at the point with position vector (2i − 3j) m and moves with constant velocity (3i + 4j) m s−1. Find its distance from the origin after 2 s.
m

Hint

Use r = r0 + vt, then find the magnitude.

Worked solution
  1. r = (2i − 3j) + 2(3i + 4j) = (8i + 5j) m.
  2. Distance = √(64 + 25) = √89 = 9.43 m (3 s.f.).
Q7Exam-style
A particle P starts at (−4i + 6j) m and moves with constant velocity (3i − j) m s−1, where i is east and j is north. Find the time at which P is due east of the origin.
s

Hint

Due east of the origin means the j component is zero and the i component is positive.

Worked solution
  1. r = (−4 + 3t)i + (6 − t)j.
  2. Due east: 6 − t = 0, so t = 6. Check: the i component is −4 + 18 = 14 > 0.
  3. t = 6 s.
Q8Challenge
A particle has initial velocity (2i − 5j) m s−1 and constant acceleration (i + 2j) m s−2. Find its speed after 4 s.
m s−1

Hint

Use v = u + at with vectors, then find the magnitude.

Worked solution
  1. v = (2i − 5j) + 4(i + 2j) = (6i + 3j) m s−1.
  2. Speed = √(36 + 9) = √45 = 6.71 m s−1 (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 · 7 points · about 10 minutes

A particle P of mass 0.5 kg is acted on by two forces, F1 = (2i − 3j) N and F2 = (4i + qj) N, where q is a constant. The resultant of the two forces is parallel to the vector (i + 2j).

  1. (a) Find the value of q.
  2. (b) Find the magnitude of the acceleration of P.
  3. (c) Find the angle between the resultant force and the vector i.

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)

Resultant = 6i + (q − 3)j. Parallel to i + 2j, so (q − 3)/6 = 2 and q = 15.

Part (b)

Resultant = (6i + 12j) N, magnitude √180 = 13.4 N. a = 13.4/0.5 = 26.8 m s−2.

Part (c)

tan θ = 12/6 = 2, so θ = 63.4°.

Your mark: 0 of 7

Common mistakes in vectors in mechanics

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