Speed and average speed

Speed describes how much distance an object travels per unit of time. A speed of $$5\ \text{m/s}$$ means that the object travels 5 metres each second.

For motion at constant speed, the speed $$v$$, distance travelled $$s$$ and time taken $$t$$ are related by:

If distance is measured in metres and time in seconds, speed is measured in metres per second, written $$\text{m/s}$$.

Average speed when speed varies

An object may travel at different speeds during a journey or stop for part of it. Its average speed describes the total distance travelled per unit of time over the whole journey:

The total time includes any time spent at rest. Average speed does not mean that the object travelled at that speed throughout the journey.

For example, suppose a person travels 120 metres in 20 seconds, rests for 10 seconds, then travels another 80 metres in 20 seconds. The total distance is 200 metres and the total time is 50 seconds, including the rest. The average speed is therefore $$200 \div 50 = 4\ \text{m/s}$$.

Scalars and vectors

Some physical quantities need only a size and a unit to describe them. Others also need a direction. The size of a quantity is called its magnitude.

A scalar has magnitude only. For example, a mass of $$5\ \text{kg}$$ does not need a direction. A vector has both magnitude and direction. For example, a force of $$5\ \text{N}$$ east is different from a force of $$5\ \text{N}$$ west.

Speed, mass and distance are scalars. Velocity, force, weight, acceleration and displacement are vectors.

Representing vectors with arrows

A vector can be represented by an arrow. The arrow’s length shows its magnitude, and the direction in which it points shows the vector’s direction. When arrows are drawn using the same scale, a longer arrow represents a greater magnitude.

Distance and displacement

Distance is the total length of the path travelled. Displacement is the change in position from the starting point to the finishing point, including its direction.

For example, if a person walks $$10\ \text{m}$$ east and then $$10\ \text{m}$$ west, the distance travelled is $$20\ \text{m}$$. The displacement is zero because the person finishes at the starting point.

Speed and velocity

Speed is the rate at which distance is travelled. Velocity is the rate at which displacement changes, so it also has a direction. A speed might be $$5\ \text{m/s}$$, whereas a velocity could be $$5\ \text{m/s}$$ east.

Mass and weight

Mass is a scalar measure of an object’s inertia: its resistance to a change in motion. Weight is the gravitational force acting on the object. Weight is a vector because the force has both a magnitude and a direction.