Scenario

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:

is the instantaneous velocity of the car (m/s)is the time in seconds is the time to reach the maximum speed in seconds 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. Identify the

1. • units of the coefficient
   • the physical meaning of A
   • the velocity of the car at t = 0
   • the asymptote of this function at → ∞?

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

1. • value x when t = 0 s
   • the asymptote of this function as t → ∞

4. Sketch a graph of position vs. time.
5. Derive an equation for the instantaneous acceleration of the car as a function of time. Identify the

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