BTEC Assignment Brief
Pearson BTEC Level 3 National Extended Diploma in Engi-
Qualification
neering
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
Learner’s name
Issue date
Hand in deadline
You are working as an apprentice engineer at a company in-
volved 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 ap-
Context prentices 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 uni-
form 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 m s−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= dsdt )
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=sin 3 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 in-
flexion.
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 dis-
−t
charging capacitor is given by v =V O e τ , where VO
is 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=12 V and τ =2 s , between t=0 s and
t=10 s .
b) Calculate the gradient at t=2 s and t=4 s .
−t
c) Differentiate 2 and calculate the value of
v =12e
dv
at t=2 s and t=4 s .
dt
d) Compare your answers for part b and part c.
e) Calculate the second derivative of the instantaneous volt-
d2 v
age
( )
dt 2
.
4 The same capacitor circuit is now charged up to 12V and
−t
the instantaneous voltage is
v =12 (1−e ) 2 .
The tasks are to:
a) Differentiate v with respect to t to give an
dv
equation for .
dt
2
BTEC Assignment Brief v1.0
BTEC Internal Assessment QDAM January 2015
Pearson BTEC Level 3 National Extended Diploma in Engi-
Qualification
neering
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
Learner’s name
Issue date
Hand in deadline
You are working as an apprentice engineer at a company in-
volved 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 ap-
Context prentices 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 uni-
form 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 m s−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= dsdt )
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=sin 3 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 in-
flexion.
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 dis-
−t
charging capacitor is given by v =V O e τ , where VO
is 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=12 V and τ =2 s , between t=0 s and
t=10 s .
b) Calculate the gradient at t=2 s and t=4 s .
−t
c) Differentiate 2 and calculate the value of
v =12e
dv
at t=2 s and t=4 s .
dt
d) Compare your answers for part b and part c.
e) Calculate the second derivative of the instantaneous volt-
d2 v
age
( )
dt 2
.
4 The same capacitor circuit is now charged up to 12V and
−t
the instantaneous voltage is
v =12 (1−e ) 2 .
The tasks are to:
a) Differentiate v with respect to t to give an
dv
equation for .
dt
2
BTEC Assignment Brief v1.0
BTEC Internal Assessment QDAM January 2015
