Movement and Position

Distance — how far something has travelled, measured in metres. It has no direction.

Speed — the distance travelled per unit time:

speed = distance ÷ time

or, as the specification writes it, v = s / t with speed in m/s, distance in m and time in s.

Velocity — speed in a stated direction. A car going 30 m/s north and one going 30 m/s south have the same speed and different velocities. This distinction only starts to matter when direction changes.

Typical speeds worth having a feel for, because "estimate" questions expect them: walking is about 1.5 m/s, cycling about 6 m/s, a car in a town about 13 m/s (30 mph), and sound in air about 340 m/s.

Distance–time graphs show distance on the vertical axis and time on the horizontal:

• A horizontal line means the distance is not changing — the object is stationary.
• A straight sloping line means constant speed.
• The gradient is the speed. A steeper line is a faster object.
• A curve means the speed is changing. Curving upwards is speeding up, curving to flatten is slowing down.

gradient = change in distance ÷ change in time

Reading the gradient of a curve — draw a tangent to the curve at the point you want, then find the gradient of that tangent. This gives the speed at one instant rather than the average.

Example: a distance–time graph that rises steeply, flattens to horizontal for thirty seconds, then rises steeply again describes a bus that drove, stopped at a stop, then drove on. The horizontal section is not the bus going nowhere in the graph's own terms — it is the bus standing still.

Average speed against instantaneous speed — the average over a journey is the total distance divided by the total time, and it can hide a great deal. A car averaging 13 m/s through a town has stopped at lights and exceeded that speed in between.