07:47 X Unit 07 - Calculus Assign... v Vocatlonll Scan-Ho 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: _+ 9U) = A(1 _ e Imam-at) v(t) is the instantaneous velocity of the car (mfs) r is the time in seconds rm\"1mm 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. Tkl 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 Pearson 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 0 Prepare a valid proposal for solving the problem and present it 0 Produce mathematical models for the identied elements of the problem 0 Apply calculus methods to produce answers for each of the elements 0 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 1. Identify the I units of the coefcientA a physical meaning of A a velocity of the car at l = l] a asymptote of this function as r ~ 3:? Sketch a graph of velocity vs. time. Derive an equation _r(i) for the instantaneous position of the car as a function of time. Identify the Q value x when l' = Cl 5 a asymptote of this function as t - 1: Sketch a graph of position vs. time. Derive an equation o(t) for the instantaneous acceleration of the car as a function of time. Identify the o acceleration of the car at: = 0 s - asymptote of this function as .t a x 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 mfs and 400m times to calculate the: o value of the coefcient A - maximum velocity a maximum acceleration. .wiv we Checklist of ouldence requlred Your informal report should contain: a written descriptions, o analysis o worked solutions to the problems 1