**Area under a graph**

Starter

I travel at 30 mph for 2 hours. Work out the distance I travel.

How does this value show itself on the speed-time graph below?

Find the area under a graph

The graph shows the velocity of a falling object plotted against the time it is falling for the first 10 seconds.

Area under a graph

The area under a graph is the opposite of the gradient of a graph (i.e. it undoes the rate of change).

For example the speed of an object is given by the gradient of a distance-time graph, and the distance the object travels is the area under the related speed-time graph.

L.O. - Interpret area under a graph for different situations and calculate/estimate areas under graphs.

Starter

I travel at 30 mph for 2 hours. Work out the distance I travel.

60 miles

How does this value show itself on the speed-time graph below?

It is the area of the rectangle.

Given that the maximum velocity of the object is 220 m/s, and that the velocity of the object after 4 seconds is 217 m/s, estimate the distance

covered by the object during the first 10 seconds of its flight.

Find the area under a graph

The graph shows the velocity of a falling object plotted against the time it is falling for the first 10 seconds.

Given that the maximum velocity of the object is 220 m/s, and that the velocity of the object after 4 seconds is 217 m/s, estimate the distance

covered by the object during the first 10 seconds of its flight.

1971 metres

Water flow against time

The graph below shows the water flow of water through a pipe when the valve controlling the pipe is turned on, and then turned off 50 seconds later.

Work out the volume of water that flows through the pipe.

Water flow against time

The graph below shows the water flow of water through a pipe when the valve controlling the pipe is turned on, and then turned off 50 seconds later.

Work out the volume of water that flows through the pipe.

150 m

3

Activity

Complete the area under the graph

worksheet.

Activity

Complete the area under the graph

worksheet.

1) 190 km

2) 12.75 m

3) 190 km

4) 8 m

5) a)Acceleration is still positive, so velocity is still increasing, so object is getting quicker.

b) i) 6 m/s

ii) 8 m/s

6) 0.7+1.13+0.64+0.64+1.17+0.52+0.4875+ 0.925 = 6.2125 kWh.

Underestimate.

Plenary

Try the exam question from the mock exam.

Plenary

Try the exam question from the mock exam.

**Activities**

**Activity**

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