Estimate Areas under graphs

Estimate Areas under graphs

GCSE(H),

When a graph shows velocity against time, the area under the graph between two points gives the distance travelled. An estimate of the area under the curve can be obtained by drawing a chord between the two points to obtain a trapezium (or, in some cases, a triangle).

Examples

1. A train accelerates away from a station as shown on the graph. After 5 seconds, the velocity of the train is 5.6m s-1. Estimate the distance covered by the train.

train accelerating from a station graph

Answer: 14m

The approximate area under a graph is given by the triangle between seconds = 0 and seconds = 5. The area is given by `frac(1)(2)` x 5 x 5.6 = 14m.

area under graph between 0 and 5 seconds

2. Using the graph above, what distance does the train travel in the next 5 seconds, if at the end of 10 seconds the train is travelling at 19ms-1?

Answer: 61.5m

The approximate area under the graph is given by `frac(1)(2)` (19 + 5.6) x 5 = 61.5m.

area under graph between 5 and 10 seconds