CSEC PHYSICS · SECTION A · LESSON A4

Scalars and Vectors: Resultants and Components

Distinguishing scalar and vector quantities, finding resultants by scale diagram and by calculation for parallel, anti-parallel and perpendicular vectors, and resolving a vector into two perpendicular components.

MechanicsA 2.1A 2.2A 2.3A 2.4≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

4 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A4 · EXPLAINER

Scalars and Vectors: Resultants and Components

A plane flying at 200 m/s north in a 50 m/s wind from the west does not travel at 250 m/s. Vectors tell us where it actually goes.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Scalar

Magnitude only: distance, speed, mass, energy, time, temperature.

Vector

Magnitude and direction: displacement, velocity, acceleration, force, weight, momentum.

Resultant

The single vector with the same effect as the vectors combined.

Parallel / anti-parallel

Add / subtract (direction of the larger).

Perpendicular

R = √(a² + b²); tan θ = opposite ÷ adjacent.

Scale diagram

Choose a scale; draw head to tail; measure R and the angle.

Components

Horizontal F cos θ; vertical F sin θ.

Equilibrium

Resultant force = 0.

EXAM TIPS & COMMON MISTAKES

  • If a quantity has a direction in the question (north, upward), treat it as a vector.
  • Pythagoras gives only the magnitude of the resultant; always give a direction as well.
  • For anti-parallel forces, subtract — and say which way the resultant acts.
  • In scale drawings state the scale and use a sharp pencil, a ruler and a protractor.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Physics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Syllabus A 2.1

1. Which of the following is a vector quantity?

Answer: D. Force has magnitude and direction.
Syllabus A 2.1

2. Which pair contains only scalar quantities?

Answer: A. Speed and distance have magnitude only.
Syllabus A 2.3

3. Forces of 6 N and 2 N act in opposite directions along the same line. The resultant is

Answer: B. 6 − 2 = 4 N in the direction of the larger force.
Syllabus A 2.3

4. Two forces of 6 N and 8 N act at right angles. The resultant magnitude is

Answer: C. √(36 + 64) = √100 = 10 N.
Syllabus A 2.4

5. A velocity of 20 m/s at 30° above the horizontal has a vertical component of

Answer: D. 20 sin 30° = 10 m/s.
Syllabus A 2.2

6. A scale diagram shows a force of 3 N using a line of 6 cm. A line of 10 cm represents

Answer: A. 1 N = 2 cm, so 10 cm = 5 N.
Syllabus A 2.3

7. The resultant of two equal and opposite forces is

Answer: B. Balanced forces give zero resultant.
Syllabus A 2.4

8. The horizontal component of a force F acting at angle θ to the horizontal is

Answer: C. The adjacent component is F cos θ.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (13 marks in total). Show all your working — method marks count. Your answers are saved on this device.

Paper 2 style · Vectors

Question 1 [13 marks]

A boat is pulled by two ropes. A calculator and a ruler may be used.

(a) (a) Distinguish between a scalar and a vector quantity. [2]

MARK SCHEME — (a) (max 2)

(b) (b) Name one scalar quantity and one vector quantity. [2]

MARK SCHEME — (b) (max 2)

(c) (c) Two forces of 30 N and 40 N act on the boat at right angles to each other. Calculate the magnitude of the resultant force. [3]

MARK SCHEME — (c) (max 3)

(d) (d) Calculate the angle the resultant makes with the 30 N force. [3]

MARK SCHEME — (d) (max 3)

(e) (e) A third force pulls the boat with 50 N directly opposite to the resultant. State the resultant of all three forces. [1]

MARK SCHEME — (e) (max 1)

(f) (f) A rope pulls with 100 N at 40° above the horizontal. Calculate the horizontal component. [2]

MARK SCHEME — (f) (max 2)

Your progress

Lesson readiness

0%
READY
Not started
Video watched (20%)0%
Multiple choice (40%)0%
Structured (40%)0%

Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.