MT1174: You are working as a Junior Engineer for a small motor racing team and You have been given a

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

2. 
   

3. units of the coefficient

4. the physical meaning of A

5. the velocity of the car at t = 0

6. the asymptote of this function at → ∞?

7. Sketch a graph of velocity vs. time.

8. Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the

9. 
   

10. value x when t = 0 s

11. the asymptote of this function as t → ∞

12. Sketch a graph of position vs. time.

13. Derive an equation for the instantaneous acceleration of the car as a function of time. Identify the

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