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# Average and Instantaneous Change

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by

## Mr Mattock

on 29 January 2017

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#### Transcript of Average and Instantaneous Change

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.
Activities
Activity