Investigating Velocity and Acceleration of the Caterham R500 Using Calculus
40091907 Chloe Catterall
Unit 7: Calculus to solve engineering problems
Assignment 3: Investigate an engineering problem using calculus
In this assignment, I will analyse a complex engineering problem by applying calculus and a mathematical problem to generate an accurate solution using data from a known model.
Caterham 7 Superlight R500
https://www.carmagazine.co.uk/car-reviews/caterham/caterham-superlight-r500-2008-review/t, (0-28 m/s) t, (440m) Tmaxspeed
2.9s 11.32s 8.0s
Caterham 7 superlight R500 (2009)
Released in 2009, the Caterham 7 Superlight R500 is a lightweight, high-performance sports car well-known for its remarkable agility and speed. The R500 has a lightweight, minimalistic design with a 2.0-liter Ford Duratec engine that generates 263 horsepower. Its lightning-fast 0-60 mph time of 2.88 seconds is achieved with a curb weight of just 506 kilogrammes (1,116 pounds). The R500 is a favourite among enthusiasts looking for a clean, track-focused roadster because of its performance, enhanced by its direct steering, superb handling, and unadulterated driving experience.
Section 1:
-10668028829000The velocity of car acceleration from rest in a straight-line equation:
V(t) is the instantaneous velocity of the car (m/s)
t is the time in seconds
Tmaxspeed is the time to reach the maximum speed in seconds
A is a constant
Unit or Component number and title
Unit 7: Calculus to solve engineering problems
Learning aim(s) (For NQF/RQF only) C: Investigate the application of calculus to solve a defined specialist engineering problem
Assignment title Investigate an engineering problem using calculus
Assessor Hand out date Hand in deadline Vocational Scenario or Context You are working as a Junior Engineer for a small motor racing team. You have been given a proposed mathematical model to calculate the velocity of a car accelerating from rest in a straight line. The equation is:
vt=A1- e-ttmaxspeed vt is the instantaneous velocity of the car (m/s)
t is the time in seconds
tmaxspeed is the time to reach the maximum speed in seconds
A is a constant.
The Team Manager has asked you to carry out an analysis of the model and produce a written report. As part of the analysis, you have been given some data on a known model.
Task 1 Produce a report that contains written descriptions, analysis and mathematics that shows how calculus can be used to solve an engineering problem. The tasks are to:
Use thinking methods to analyse the given engineering problem, e.g. break the problem down into a series of manageable elements, and produce a specification
Prepare a valid proposal for solving the problem and present it
Produce mathematical models for the identified elements of the problem
Apply calculus methods to produce answers for each of the elements
Bring the elements together in a formal presentation
In your proposal you need to outline the problem and the methods needed to solve it. You need to include how to
Identify the:
units of the coefficient A
physical meaning of A
velocity of the car at t=0
asymptote of this function as t?
Sketch a graph of velocity vs. time.
Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the
value xwhen t=0s
asymptote of this function as t
Sketch a graph of position vs. time.
Derive an equation at for the instantaneous acceleration of the car as a function of time. Identify the:
acceleration of the car at t=0s
asymptote of this function as t
Sketch a graph of acceleration vs. time.
Apply your mathematical models to your allocated car. Use the given data for the 0 28 m/s and 400m times to calculate the:
value of the coefficient A
maximum velocity
maximum acceleration.
Checklist of evidence required Your informal report should contain:
written descriptions,
analysis
worked solutions to the problems
Each worked solution should be laid out clearly and contain brief explanations of the stages of the calculation to indicate your understanding of how calculus can be used to solve an engineering problem. Diagrams and sketches should be well presented and clearly labelled.
Criteria covered by this task:
Unit/Criteria reference To achieve the criteria you must show that you are able to:
C. P7 Define a given engineering problem and present a proposal to solve it.
C. P8 Solve, using calculus methods and a mathematical model, a given engineering problem.
C. M3 Analyse an engineering problem, explaining the reasons for each element of the proposed solution.
C. M4 Solve accurately, using calculus methods and a mathematical model, a given engineering problem.
C. D3 Critically analyse, using technically correct language and a logical structure, a complex engineering problem, synthesising and applying calculus and a mathematical model to generate an accurate solution.
Sources of information to support you with this Assignment Websites
http://www.mathsisfun.com/index.htmhttp://www.mathcentre.ac.uk/students/topicsOther assessment materials attached to this Assignment Brief Table of 0-28 m/s, 400m and time to reach maximum speed times.
