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Instantaneous Rates of Change

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by

Mr Mattock

on 28 January 2017

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Transcript of Instantaneous Rates of Change

Instantaneous Rates of Change
Starter
This graph shows the height of a ball that is thrown in the air, against the time it is in the air.
Example
The graph shows the concentration of reactant present in a solution during a chemical reaction as time increases.

Work out the rate of reactant loss after 7 seconds.
Instantaneous rates of change
What is the velocity of the object after 2 mins?

After 3 mins?
L.O. - Use a tangent to find the rate of change of a graph at an instant.
(a) Explain why the velocity of ball is always changing.

(b) Explain how you know that the velocity of the ball is positive at the beginning and negative at the end.

(c) Explain why there must be an instant when the velocity of the ball is 0.
Starter
This graph shows the height of a ball that is thrown in the air, against the time it is in the air.
(a) Explain why the velocity of ball is always changing.
Graph is curved
(b) Explain how you know that the velocity of the ball is positive at the beginning and negative at the end.
Height gets bigger over time at beginning and smaller over time at the end.
(c) Explain why there must be an instant when the velocity of the ball is 0.
There is a point when the ball stops travelling up and starts travelling down.
Instantaneous rates of change
What is the velocity of the object after 2 mins?

After 3 mins?
Instantaneous rates of change
What is the velocity of the object after 2 mins?

62 - 40
2.25 - 0

After 3 mins?
= 2.7777...
= -2.7777...
Example
The graph shows the concentration of reactant present in a solution during a chemical reaction as time increases.

Work out the rate of reactant loss after 7 seconds.

0.125 - 0.07 0.55
8.5 - 4.5 4
= = 0.135
Activity
Complete the worksheet on tangents and gradients.
Activity
Complete the worksheet on tangents and gradients.

1) (a) (i) gradient = 2 (ii) gradient = -2
(b) gradient = 0

2) Gradients are 2, 4, 6, -2, -4 respectively. The gradient can be found by doubling the x-coordinate.

3) Gradients are 5, 7, 9, 1, -1. 2x + 3 gives the gradient of the curve at any point.

4) Gradient = 11. Gradient is -11 at x = -3.5.

Activities
Activity
Answers

Key
Examples

Worked
Example
Part 1

Worked
Example
Part 2

Worked
Example
Full transcript