BTEC Assignment Brief
Pearson BTEC Level 3 National Extended Diploma in
Engineering
Pearson BTEC Level 3 National Extended Diploma in
Electrical/Electronic Engineering
Pearson BTEC Level 3 National Extended Diploma in
Mechanical Engineering
Qualification
Pearson BTEC Level 3 National Extended Diploma in
Computer Engineering
Pearson BTEC Level 3 National Extended Diploma in
Manufacturing Engineering
Pearson BTEC Level 3 National Extended Diploma in
Aeronautical Engineering
Unit number and title Unit 7: Calculus to solve engineering problems
A: Examine how differential calculus can be used to solve
Learning aim(s) (For NQF
engineering problems
only)
Solving engineering problems that involve differentiation
Assignment title
Assessor Md Nur-E-Alam Khan
Issue date
11/11/2021
01/12/2021
Hand in deadline
You are working as an apprentice engineer at a company
involved in the research, design production and
maintenance of bespoke engineering solutions for larger
customers.
Part of your apprenticeship is to spend time working in all
departments, however a certain level of understanding
Vocational Scenario or
needs to be shown before the managing director allows
Context
apprentices into the design team and so she has developed
a series of questions on differentiation to determine if you
are suitable.
Task 1 Produce a report that contains written descriptions, analysis
and mathematics that shows how calculus can be used to
solve engineering problems as set out below.
1 The equation for a distance, s(m), travelled in time t(s)
, by an object starting with an initial velocity u(ms-1) and
uniform acceleration a(ms-2) is:
1
s=ut+ a t 2
2
The tasks are to:
a) Plot a graph of distance (s) vs time (t) for the first
10s of motion if u=10 ms−1 and a=5 m s−2.
b) Determine the gradient of the graph at t =2 s and
t=6 s.
c) Differentiate the equation to find the functions for
i) (
Velocity v=
ds
dt )
( )
2
dv d s
ii) Acceleration a= =
dt dt 2
d) Use your result from part c to calculate the velocity
at t =2 s and t=6 s.
e) Compare your results for part b and part d.
2 The displacement of a mass is given by the function
y=sin3 t .
The tasks are to:
a) Draw a graph of the displacement y(m) against time
t(s) for the time t=0 s to t=2. s .
b) Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
3 The equation for the instantaneous voltage across a
−t
discharging capacitor is given by v=V e τ , where V O is
O
the initial voltage and τ is the time constant of the
circuit.
The tasks are to:
a) Draw a graph of voltage against time for V O =12V
2
BTEC Assignment Brief v1.0
BTEC Internal Assessment QDAM January 2015
Pearson BTEC Level 3 National Extended Diploma in
Engineering
Pearson BTEC Level 3 National Extended Diploma in
Electrical/Electronic Engineering
Pearson BTEC Level 3 National Extended Diploma in
Mechanical Engineering
Qualification
Pearson BTEC Level 3 National Extended Diploma in
Computer Engineering
Pearson BTEC Level 3 National Extended Diploma in
Manufacturing Engineering
Pearson BTEC Level 3 National Extended Diploma in
Aeronautical Engineering
Unit number and title Unit 7: Calculus to solve engineering problems
A: Examine how differential calculus can be used to solve
Learning aim(s) (For NQF
engineering problems
only)
Solving engineering problems that involve differentiation
Assignment title
Assessor Md Nur-E-Alam Khan
Issue date
11/11/2021
01/12/2021
Hand in deadline
You are working as an apprentice engineer at a company
involved in the research, design production and
maintenance of bespoke engineering solutions for larger
customers.
Part of your apprenticeship is to spend time working in all
departments, however a certain level of understanding
Vocational Scenario or
needs to be shown before the managing director allows
Context
apprentices into the design team and so she has developed
a series of questions on differentiation to determine if you
are suitable.
Task 1 Produce a report that contains written descriptions, analysis
and mathematics that shows how calculus can be used to
solve engineering problems as set out below.
1 The equation for a distance, s(m), travelled in time t(s)
, by an object starting with an initial velocity u(ms-1) and
uniform acceleration a(ms-2) is:
1
s=ut+ a t 2
2
The tasks are to:
a) Plot a graph of distance (s) vs time (t) for the first
10s of motion if u=10 ms−1 and a=5 m s−2.
b) Determine the gradient of the graph at t =2 s and
t=6 s.
c) Differentiate the equation to find the functions for
i) (
Velocity v=
ds
dt )
( )
2
dv d s
ii) Acceleration a= =
dt dt 2
d) Use your result from part c to calculate the velocity
at t =2 s and t=6 s.
e) Compare your results for part b and part d.
2 The displacement of a mass is given by the function
y=sin3 t .
The tasks are to:
a) Draw a graph of the displacement y(m) against time
t(s) for the time t=0 s to t=2. s .
b) Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
3 The equation for the instantaneous voltage across a
−t
discharging capacitor is given by v=V e τ , where V O is
O
the initial voltage and τ is the time constant of the
circuit.
The tasks are to:
a) Draw a graph of voltage against time for V O =12V
2
BTEC Assignment Brief v1.0
BTEC Internal Assessment QDAM January 2015
