Rate of change

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From users who are not members of Introduction to differentiation :

Jo-Ann Lyons

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Ready to use

6 years, 2 months ago

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Jo-Ann Lyons 6 years, 2 months ago

Gave some feedback: Ready to use

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Frank Doheny 8 years, 5 months ago

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Frank Doheny 8 years, 7 months ago

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Name	Status	Author	Last Modified
Rate of change	Ready to use	Frank Doheny	13/03/2019 15:25
Katy's copy of Rate of change	Ready to use	Katy Dobson	30/07/2018 12:14
Simon's copy of Rate of change	draft	Simon Thomas	14/03/2019 11:13
Maria's copy of Rate of change	draft	Maria Aneiros	27/05/2019 05:47
Rate of change	draft	Xiaodan Leng	10/07/2019 22:14
Musa's copy of 3 Rate of change	draft	Musa Mammadov	27/06/2023 01:33
Musa's copy of 3 simple derivatives	draft	Musa Mammadov	27/06/2023 01:34

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Question statement

A missile is launched straight up in the air. The height of the missile, $h$ metres, above the ground $t$ seconds after the launch button is pressed is given by:

$h=\var{a}t-4.9t^2$

Give any introductory information the student needs.

			Name	Type	Generated Value

			a	integer	230
			b	integer	9

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

230

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Calculate the speed of the missile (m/s) $\var{b}$ seconds after launch. Give your answer correct to one decimal place.

$v =$ Gap 0.m/s

What is the maximum height achieved by this missile? Give your answer correct to one decimal place.

$h =$ Gap 1.m

Advice

$h=\var{a}t-4.9t^2$

Recall that speed is the rate of change of position with respect to time i.e. $v=\frac{dh}{dt}$

$v=\frac{dh}{dt}=\var{a}-2*4.9t$

when $t=\var{b}$

$v=\var{a}-2*4.9*\var{b}$

$v=\simplify{{a}-9.8*{b}}m/s$

The missile will reach its maximum height when its speed = 0. i.e. $v=\frac{dh}{dt}=\var{a}-2*4.9t=0$

$\var{a}=9.8t$

$t=\var{a}/9.8$

The maximum height reached will occur when $t=\simplify{{a}/9.8}$

$h=\var{a}*\left(\simplify{{a}/9.8}\right)-4.9*\left(\simplify{{a}/9.8}\right)^2$

$h=\simplify{{a}^2/19.6}$

$h=\simplify{{{a}/{19.6}^0.5}^2}$

Give a worked solution to the whole question.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Jo-Ann Lyons 6 years, 2 months ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Rate of change

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jo-Ann Lyons 6 years, 2 months ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`