**Average and Instantaneous Change**

Starter

The graph shows distance travelled against the time take for a baseball player running to first base. Find the speed of the player after 0.7 seconds.

Average and Instantaneous Change

The instantaneous rate of change of one variable with respect to another is equal to the gradient of the tangent drawn to the graph of the variables at the required point.

The average rate of change of one variable with respect to another is equal to the gradient of the chord drawn between the two points on the graph of the variables between which the average is being calculated.

Example

The graph shows the distance travelled against the time taken for a baseball player to run to first base. Find the player's average speed whilst running.

L.O. - Understand the difference average and instantaneous rates of change, and calculate average rates of change.

Starter

The graph shows distance travelled against the time take for a baseball player running to first base. Find the speed of the player after 0.7 seconds.

12

1.4

= 8.57

ft/sec

Example

The graph shows the distance travelled against the time taken for a baseball player to run to first base. Find the player's average speed whilst running.

15

1.5

= 10

ft/sec

Example

The graph shows the light intensity measured from a light source that is steadily moved away from the light sensor. Find the average rate of decrease of light intensity with respect to distance over:

(a) the first 20 centimetres

(b) the first 40 centimetres

(c) the whole 80 centimetres

Example

The graph shows the light intensity measured from a light source that is steadily moved away from the light sensor. Find the average rate of decrease of light intensity with respect to distance over:

(a) the first 20 centimetres

50-13

20

(b) the first 40 centimetres

50-5

40

(c) the whole 80 centimetres

50-2

80

= 1.85

cd/cm

= 1.125

cd/cm

= 0.6

cd/cm

Activity

Complete the worksheet

Activity

Complete the worksheet

1) Yes, 12km/h averaged.

2) 0.6 grams per week

3) (a) 0.6 m/s (b) between 11-14 seconds

4) (a) 0.0073 g/s (b) 0.006g/s

5) (a) 0.8 degrees/min (b) 0.37 degrees/min

(c) 0.13 degrees/min (d) 0.37 degrees/min

6) (a) 2.89 people/day (b) 69.4 people/day

(c) Because at the rate it is rising the whole world would be infected in a few months.

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