Topic 5 of 5
Scalars and vectors
A scalar has magnitude only. A vector has both magnitude and direction.
Magnitude means size, given by a numerical value and its unit where applicable. A speed of 4 m/s tells us how fast an object moves. A velocity of 4 m/s east also tells us its direction.
| Scalar | Related vector |
|---|---|
| Distance: total length of the path travelled. | Displacement: change in position from start to finish, including direction. |
| Speed: distance travelled per unit time. | Velocity: rate of change of displacement, including direction. |
| Mass: a property measured in kilograms. | Weight: the gravitational force on an object, measured in newtons (N). Near Earth it acts downwards. |
Time, temperature and energy are also scalars. Force and acceleration are vectors. Acceleration describes a change in velocity per unit time, so the direction of that change matters.
Compare the descriptions
Same magnitude does not mean the same vector
Two cyclists each have a speed of 4 m/s. One travels east and one west. Their speeds are equal, but their velocities differ because they point in opposite directions.
If east is chosen as positive along a straight line, the velocities can be written as +4 m/s and -4 m/s. The signs now encode the chosen directions; both magnitudes are 4 m/s.
A minus sign alone does not make a quantity a vector. A temperature of -5 °C is still a scalar. The value is below zero on the Celsius scale; it does not point in a spatial direction.
In a vector answer, state the direction as well as the magnitude, such as 6 N upwards. For signed values, say which direction you have taken as positive.