You have been given a proposed mathematical model to calculate the velocitv of a car accelerating from rest in a straight line. The equation is: I so) = A (1 armed) v(t) is the instantaneous velocity of the car (ml's) r is the time in seconds t,,,,,,,,,,,,,,,,I is the time to reach the maximum speed in seconds A is a constant. tf4n1 tuna-arson m_ _,__ 5 .4 randE-ortwtesse not: \"ZIIEII 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 specication Prepare a valid proposal for solving the problem and present it Produce mathematical models for the identied elements of the problem Applv calculus methods to produce answers for each of the elements Bring the elements together in a formal presentation 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 - co? 2. Sketch a graph of velocity vs. time. 3. Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the . value x when t = 0 s . asymptote of this function as t - co4. 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 - co 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