# 5.1.1 Scalars & Vectors

### Scalars & Vectors

• All quantities can be one of two types:
• A scalar
• A vector

#### Scalars

• Scalars are quantities that have only a magnitude
• For example, mass is a scalar quantity since it is a quantity that has no direction to it

#### Vectors

• Vectors have both a magnitude and a direction
• Velocity is a vector quantity since it is described with both a magnitude and a direction
• When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling
• For example, 60 km per hour in a Westerly direction
• Distance is a value describing only how long an object is or how far it is between two points – this means it is a scalar quantity
• Displacement on the other hand also describes the direction in which the distance is measured – this means it is a vector quantity
• For example, 100 km in a Northern direction

#### Comparing Scalars & Vectors

• The table below lists some common examples of scalar and vector quantities:

Scalars & Vectors Table • Some vectors and scalars are similar to each other
• For example, the scalar quantity distance corresponds to the vector quantity displacement
• Corresponding vectors and their scalar counterparts are aligned in the table where applicable

#### Exam Tip

Do you have trouble figuring out if a quantity is a vector or a scalar? Just think – can this quantity have a minus sign? For example – can you have negative energy? No. Can you have negative displacement? Yes!

Make sure you are comfortable with the differences between similar scalars and vectors, the most commonly confused pairings tend to be:

• Distance and displacement
• Speed and velocity
• Weight and mass

### Representing Vectors

• A vector can be represented by using an arrow
• The length of the arrow represents the magnitude of the vector
• The direction of the arrow indicates the direction of the vector Two forces represented by arrows.
Force A has a larger magnitude than Force B. Force A is directed to the right and slightly upwards, whereas Force B is directed to the left and slightly upwards.

#### Worked Example

A tennis ball is thrown at an angle of 45° to horizontal at a speed of 5 m/s. A second tennis ball is thrown in the same direction at a speed of 10 m/s.

Draw the velocity vectors of the balls.

Step 1: Draw the first tennis ball and its velocity vector

• Measure the 45° angle with a protractor Step 2: Draw the second tennis ball and its velocity vector

• The second ball has a speed of 10 m/s, so the arrow will be twice as long  ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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