Vectors and Scalars

Edexcel Statements

A scalar quantity is a quantity that has magnitude only and has no direction in space

Examples of Scalar Quantities:

Length Area Volume Time Mass

Examples of vector quantities:

Displacement Velocity Acceleration Force

V

Distance and Displacement

Distance is the total length of path travelled

scalar

Displacement is the length of and direction of a straight line from the starting point to the finishing point.

vector

Unit needed

Unit and direction needed

Speed and velocitySpeed is the rate of change of distance (scalar)

Displacement is the rate of change of displacement (vector)

• Vector diagrams are shown using an arrow

• The length of the arrow represents its magnitude

• The direction of the arrow shows its direction

Vector Diagrams

Adding vectors

• Two (or more) vector quantities may be added using the ‘tip to tail’ rule.

• The single vector obtained is the resultant vector

You need to be able to add vectors both diagrammatically (using a scale drawing ) or mathematically, using trigonometry.

Vectors in opposite directions:6 m s-1 10 m s-1 = 4 m s-1

6 N 10 N = 4 N

Resultant of Two Vectors – simplest case

Vectors in the same direction:

6 N 4 N = 10 N

=

The tip to tail rule

• Each vector is represented as a straight line with an arrow to show the direction.

• The vectors are joined so that the tip of the first vector (or previous) touches the tail of the second (or next) vector.

• A straight line is drawn from the starting point to the finishing point (the resultant).

Triangle Law

Parallelogram Law

Example 1A person travels 300 m North and 400 m East. What is the resultant displacement?

Example 2