Hnc mechanical Engineering Maths

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Higher National Assessment Designed in accordance with HEA guidelines

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Learner Name: Year of Course 1

Programme Title Pearson BTEC Level 4/5 Higher National Certificate/Diploma in Engineering (RQF)

Programme No BBYH8 - BBYH9 - BBYJ1 DBMT1 – DBMT4

Unit Title 2. Engineering Maths (L4) Unit Code M/615/1476

Assignment Title Calculus Assignment No 3 of 3

Author Michael Lopez Assessor Engineering Team Internal Verifier Jamie Caulfield Verification Date 2nd April 2021

Week of Issue Due Week Date Submitted Agreed Resubmission Date Date Resubmitted 29 32

Please append your answers to the end of this brief. Include ALL pages of this brief in your submission. Do not submit separate documents unless requested. PLEASE NOTE: Provide a Table of Contents for your answers, indicating the page number for each of these. Please also provide inline references for your sources of information and a REFERENCES section at the end of the work, where appropriate, using the Harvard Referencing System.

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Relevant Learning Outcomes and Assessment Criteria Pass Merit Distinction

LO4: Examine how differential and integral calculus can be used to solve engineering problems

D3 Analyse maxima and minima of increasing and decreasing functions using higher order derivatives.

P8 Determine rates of change for algebraic, logarithmic and circular functions.

M4 Formulate predictions of exponential growth and decay models using integration methods.

P9 Use integral calculus to solve practical problems relating to engineering.

Unit Learning Outcomes LO4: Examine how differential and integral calculus can be used to solve engineering problems

Assignment Brief and Guidance Scenario: You work as a technical analyst for a large publisher of engineering text books. One of their well- known authors has set a number of further problems in her latest draft engineering text, aimed at the level four engineering market. She wishes to set these further problems throughout the text and intends to provide the worked solutions on a companion website for the new book. The author has asked you to provide these worked solutions. The further problems are given in the following tasks: - Activity Task 1:

Differentiate each of the following voltage functions with respect to time and hence determine the ‘rate of change’ for each of the functions when time (t) is 5 seconds.

a) 𝑣𝑣 = (𝑡𝑡2 + 6)2

b) 𝑣𝑣 = (3𝑡𝑡3 − 4𝑡𝑡 + 6)3

c) 𝑣𝑣 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒(2𝑡𝑡)

d) 𝑣𝑣 = 4𝑒𝑒−0.5𝑡𝑡

e) 𝑣𝑣 = sin(2𝑡𝑡3 + 4𝑡𝑡 − 2)

f) 𝑣𝑣 = cos(3𝑡𝑡4 − 5𝑡𝑡 + 4) Task 2: PART 1 For the circuit shown below, assuming zero charge on the capacitor at t = 0, the current flowing may be quantified as…

t RCEi e

−

Integrate this equation with respect to t and hence find the charge stored in the capacitor one second after the switch is closed.

PART 2 The current (𝑖𝑖𝐿𝐿) through a 10 mH inductor (L) has a relationship with time (t) as follows;

𝑖𝑖𝐿𝐿 = 1 𝐿𝐿 � cos(100𝑡𝑡) 𝑑𝑑𝑡𝑡

Determine the inductor current when the time is 0.9 seconds. Task 3: PART 1 Determine the area under the following exponential growth curve between 2 seconds and 4 seconds;

𝑦𝑦 = �(1 − 𝑒𝑒−𝑡𝑡) 4

𝑑𝑑𝑡𝑡

PART 2 Determine the area under the following exponential decay curve between 2 seconds and 4 seconds;

𝑦𝑦 = �(𝑒𝑒−𝑡𝑡) 4

𝑑𝑑𝑡𝑡

Task 4: PART 1 Locate the co-ordinates of the turning point for the following function and determine whether it is a maxima or minima;

𝑦𝑦 = 3𝑥𝑥2 − 5𝑥𝑥 PART 2 Find the maxima and minima values for the function;

𝑦𝑦 = 𝑥𝑥3 − 4𝑥𝑥 + 6

ANSWERS...

Higher National Assessment
Designed in accordance with HEA guidelines