What is covered in Grade 10 Physical Sciences Vectors and Scalars?

A scalar has magnitude only; a vector has both magnitude and direction. Vectors can be added graphically using the head-to-tail method. The resultant is the single vector that has the same effect as the original set.

What is Scalar in Physical Sciences?

A physical quantity that has magnitude only (size), and no direction. Examples: distance, speed, mass, temperature.

What is the formula for Resultant (collinear, same direction)?

The formula for Resultant (collinear, same direction) is: R = A + B. Where: R = resultant, A and B = magnitudes of vectors in the same direction

Is Grade 10 Physical Sciences Vectors and Scalars on the CAPS curriculum?

Yes. Vectors and Scalars is part of the official CAPS Physical Sciences curriculum for Grade 10, Term 3 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Vector Head-to-Tail Method

Q: What is Vector?

A physical quantity that has both magnitude and direction. Examples: displacement, velocity, acceleration, force.

Every measurement in physics is either a scalar (just a size) or a vector (size AND direction). Understanding the difference is the foundation of all mechanics.

Week 4

Scalars, Vectors and the Resultant

Distinguish scalar from vectorDefine resultantAdd collinear vectorsUse the head-to-tail method

Definition

Scalar

A scalar is a physical quantity that has magnitude (size) only, and no direction. Examples: distance, speed, mass, temperature, time, energy.

Definition

Vector

A vector is a physical quantity that has both magnitude and direction. Examples: displacement, velocity, acceleration, force, weight.

Definition

Resultant

The resultant is the single vector that produces the same effect as two or more vectors combined.

Δx

Definition

Displacement (Δx)

Displacement is the change in position of an object; a vector quantity with magnitude (distance) and direction.

Figure 17.1 — Head-to-tail method for adding collinear vectors. The tail of the second vector is placed at the head of the first. The resultant runs from the tail of the first vector to the head of the last vector. For vectors in opposite directions, the resultant is the algebraic sum.

Scalars vs Vectors

Property	Scalar	Vector
Has direction?	No — magnitude only	Yes — magnitude AND direction
Addition method	Normal arithmetic	Head-to-tail or algebraic with signs
Examples	Distance, speed, mass, time	Displacement, velocity, force

To add collinear (same line) vectors: choose a positive direction, assign positive signs to vectors in that direction and negative signs to vectors in the opposite direction, then add algebraically. The sign of the result tells you the direction.

ℹ

Note

In Grade 10, we only add collinear vectors (vectors along the same straight line). Grade 11 introduces vectors at angles using the Pythagorean theorem and trigonometry.

Worked Example

A learner walks 8 m East then 5 m West. Find the resultant displacement.

Given

8 m East
5 m West

Find

Resultant displacement

Solution

1Choose East as positive (+)
28 m East = +8 m
35 m West = −5 m
4R = +8 + (−5) = +3 m
5Positive sign means the resultant is in the East direction

Answer: R = 3 m East

Worked Example

Three forces act on an object in a straight line: 15 N East, 20 N East, 8 N West. Find the resultant force.

Given

15 N East
20 N East
8 N West

Find

Resultant force

Solution

1Take East as positive (+)
2R = +15 + (+20) + (−8)
3R = +27 N
4Positive → resultant is East

Answer: R = 27 N East

Practice Question

A car drives 50 km North, then 20 km South, then 15 km North. Calculate the resultant displacement.

(4 marks)

Practice Question

Two tugboats pull a ship. Tug A applies 5 000 N East; Tug B applies 3 000 N West. Calculate the resultant force and state its direction.

(3 marks)