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: v(t)=A(1-e^t/t_maxspeed )

v(t) is the instantaneous velocity of the car(m / s)

t is the time in seconds

t_maxspeed 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.

Data:

Car Model = Bugatti Veyron t(0-28m/s)(s) = 2.5

t(400m) = 9.75

t_maxspeed(s) = 8.0

However, the time taken to reach the steady state value (maximum speed) is approximately 5 time constants, so the model as it stands cannot work accurately. A modified model recognising this issue would be to change it to

: v =A(1-e^-5t/t_maxspeed)

Produce a report that contains written descriptions, analysis and mathematics that shows how calculus can be used to solve an engineering problem. Your Answer must include :

methods to analyse the given engineering problem

a valid proposal for solving the problem and present it

Apply calculus methods to produce answers for each of the elements

Bring the elements together in a formal presentation(most important)

Your Question:

1. 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

2. Sketch a graph of position vs. time.