Speed, Motion Graphs, and Vectors

Speed tells you how fast something moves, calculated by dividing distance by time. For average speed, you can also add the initial and final speeds together, then divide by 2 - dead simple!

Motion graphs are your best friends for visualising movement. Distance-time graphs show how far an object has travelled over time, whilst speed-time graphs reveal how the object's speed changes. The steeper the line, the faster the change!

Here's where it gets interesting: scalars only have size (like distance and speed), but vectors have both size and direction (like displacement and velocity). Think of it this way - if you walk 5 metres, that's distance (scalar), but if you walk 5 metres north, that's displacement (vector).

Rate of Change (ROC) measures how quickly speed changes over time, calculated as (final speed - initial speed) ÷ time taken. This gives you acceleration in m/s².

Quick Tip: Remember that velocity is just speed with direction - so 30 m/s east is velocity, whilst 30 m/s is just speed!

Acceleration shows how quickly velocity changes, using the formula a = $v-u$/t, where 'v' is final velocity, 'u' is initial velocity, and 't' is time. When objects slow down, we call it deceleration (negative acceleration).

For displacement-time and velocity-time graphs, the area under the curve gives you distance travelled, whilst the gradient tells you the rate of change. These graphs help you spot when objects are moving at constant speed, accelerating, or decelerating just by looking at the line's shape.