Distance from the area under a velocity-time graph

In this lesson

Find the distance travelled from the area enclosed by a velocity-time graph, including by counting squares when the line is a curve.

What it covers

• The area under a velocity-time graph is the distance travelled - stated in the same sentence shape as the two gradient sentences
• WHY it is, argued in one step rather than asserted: a thin vertical strip of the graph is a velocity multiplied by a small time, which is a distance, and the whole area is all the strips added up
• The constant-velocity case first: a rectangle, area = velocity x time, which is just distance = speed x time drawn as a picture
• The uniform acceleration case: a triangle, area = half x base x height
• A real journey as a rectangle plus a triangle, or as a trapezium, with the two parts added and the working shown
• Counting squares under a CURVE: work out what ONE square is worth first, from the two axis scales, then count whole squares and count part-squares over half
• The unit falling out of the multiplication: metres per second multiplied by seconds gives metres, every time, which is the check that the area is a distance
• Reading the question for WHICH interval is being asked about, and shading only that region
• The decision rule, stated once and kept on screen: gradient tells you how fast it is changing, area tells you how far it has gone

Key words

On the specification