Describing motion with graphs — Physics, 14–17 years
Position–time and velocity–time graphs turn a journey into a picture. Their slopes and areas reveal how an object moves without showing every moment separately.
What the graphs mean
A position–time graph shows where an object is at each moment. A steeper line means greater speed, and a horizontal line means the object is stopped. On a velocity–time graph, the slope tells you acceleration and the area under the line tells you distance travelled.
Why use graphs?
A list of measurements can hide the pattern in a journey. Scientists needed a quick way to compare starts, stops and speeding up, so they plotted position or velocity against time. The graph lets you estimate what happened between measurements, while keeping the units visible.
Worked example
A cyclist’s velocity rises from 0 to 6 m/s in 3 s, then stays at 6 m/s for 2 s. First, the acceleration is the slope: 6 ÷ 3 = 2 m/s². The distance is the triangle area, ½ × 3 × 6 = 9 m, plus the rectangle area, 2 × 6 = 12 m. Total: 21 m.
The common mistake
People often read the height of a velocity–time graph as the distance. That feels reasonable because a taller graph looks like more movement. But height is velocity at one instant; distance is the whole area beneath the graph, so both time and velocity matter.
Where it is used
Cycling computers and fitness watches record speed against time to show a route’s effort. Engineers use the same graphs to test lifts, trains and cars, checking whether acceleration is safe and comfortable. GPS apps usually add position–time data to compare journeys.
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