4.5.6.1.3 - Velocity

Velocity is speed in a direction

Speed tells you how fast something is moving. Velocity tells you how fast something is moving in a particular direction.

A speed such as 12 m/s can be a complete value. It tells you the rate of movement, but not where the object is heading.

A velocity needs the direction as well:

Velocity is a vector quantity because it has magnitude and direction. The magnitude of a velocity is the speed value, such as 12 m/s. The direction might be written as a compass direction, such as east, or as a clear direction in context, such as upwards, towards the wall or away from the start line.

Distance, displacement, speed and velocity

The vector-scalar distinction is especially important for four motion quantities:

Distance is how far an object moves. It does not include direction, so it is a scalar quantity. For example, a student might walk a distance of 200 m during a lap of a field.

Displacement is the straight-line change in position from the start point to the finish point, including direction. It is a vector quantity. For example, after walking across a field, a student's displacement might be 120 m north-east from the starting point.

Speed and velocity follow the same pattern. Speed does not involve direction, so it is scalar. Velocity includes direction, so it is vector.

Same unit, different meaning

The unit alone does not tell you whether a quantity is a scalar or a vector.

Distance and displacement are both measured in metres, m. Speed and velocity can both be measured in metres per second, m/s. The difference is not the unit; the difference is whether direction is part of the quantity.

For example, 50 m could be a distance if it means the length of a path travelled. 50 m west is a displacement because it gives the straight-line change in position and the direction. In the same way, 4 m/s is a speed, while 4 m/s west is a velocity.