Interpret Gradients and Areas in Context
# Interpret Gradients and Areas in Context

GCSE(H),

A gradient for a graph gives the *rate of change* of the item being measured. The area under a graph gives the amount *consumed* over an interval.

If the measurement is distance, then the rate of change of distance is velocity. If the measurement is velocity, then the rate of change gives acceleration. If the measurement is velocity, then the area gives the distance.

## Examples

1. The graph shows the performance of two similar engines. One runs at a higher rate of rpm (revolutions per minute) than the other. Which engine configuration has the higher rate of acceleration at 5 seconds?

Answer: Low RPM

At 5 seconds, the gradient for High RPM is `frac(3.850-2.650)(4)` = 0.300 ms^{-2}. For Low RPM the gradient is `frac(3.200-1.800)(4)` = 0.350ms^{-2}.

2. What distance does the low RMP engine cover in the first 5 seconds?

Answer: 12.5m

The distance covered is the area under the graph for the first 5 seconds. The area is 2.500 x 5 = 12.500 metres.

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