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: f 13(t) : A(1 _ E tmoxspeed) 1:03;) is the instantaneous velocity of the car (m/s} I is the time in seconds tmnxspeed 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. A car model (Caparo T1 2.4 V0 - [2006]) has been carried out by a candidate of a company. The car model gives the data below: tm-zs mis} t(4oom) (S) (S) l(Star modal Caparo T1 2.4 V8 - [2006] 2.5 8.23 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: 0 Use thinking methods to analyse the given engineering problem, e.g. break the problem down into a series of manageable elements, and produce a specication Prepare a valid proposal for solving the problem and present it Produce mathematical models for the identied elements of the problem Apply calculus methods to produce answers for each of the elements Bring the elements together in a formal presentation our proposal you need to outline the problem and the methods needed to solve it. You need to include how to 1. Identify the units of the coefficient A physical meaning of A . velocity of the car at t = 0 asymptote of this function as t - o? 2. Sketch a graph of velocity vs. time. 3. Derive an equation s() for the instantaneous position of the car as a function of time. Identify the . value s when t = 0 s . asymptote of this function as t - co 4. Sketch a graph of position vs. time. 5. Derive an equation a(t) for the instantaneous acceleration of the car as a function of time. Identify the acceleration of the car at t = 0 s asymptote of this function as t - go 6. Sketch a graph of acceleration vs. time. 7. 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 Your informal report should contain: required 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