Describing Motion Around Us

Picture a dog fetching a ball thrown straight down a long, flat park path. The ball lands 30 m from where the dog started. The dog runs the full 30 m to reach it, then trots back only 10 m before deciding to stop and chew on it for a while.

You already know average speed, the total distance covered divided by the time taken, but speed on its own never tells you which way something is going, only how quickly ground is being covered.

Velocity itself can change over time, sometimes gradually, sometimes suddenly, and the quantity that captures how quickly it changes is called acceleration.

Numbers in a table are useful, but a graph often reveals a motion's true character at a glance.

Velocity-time graphs work the same way, but now plot an object's velocity against time instead of its position, and they reveal a different kind of information.

For the special, common case of motion with constant acceleration in a straight line, the relationships between an object's initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s) can all be captured in three compact equations: v = u + at, which finds a final velocity; s = ut + ½at², which finds displacement directly from time; and v² = u² + 2as, which finds a final velocity without needing time at all, useful whenever time was not measured or is not the quantity you need.