Corolla Assignment

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|Year 12 Math C assignment |
|Overtaking |
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The problem

Aim: To find
Based on the 10m on the graph given.

Assumptions: • Refer to the assumptions made in Case 1.0 • Based on the 10m

The distance between the two cars is still assumed to be 46m in this case. Refer to Case 1.0 for calculation

The velocity equation of corolla for this case can be calculated as follows:
[pic]
[pic] m = [pic] m = 4.5

[pic] y-100 = 4.5( x -10) y = 4.5x -45+100 y = 4.5 x + 55

Since it is a velocity equation, this can also be written as: v= 4.5t + 55
The numbers are in km/h. Therefore it is converted into m/s. (International System of Units) v=[pic] v= 1.25t + 15.28
[pic]The velocity for corolla is 1.25t + 15.28
[pic]

Once the velocity is found, the displacement and the acceleration of corolla can also be found using calculus.
The acceleration of corolla is found by differentiation.
V= 1.25t + 15.28
A = [pic]
A= 1.25m[pic]
[pic]Corolla accelerates at 1.25ms-2

The displacement of the corolla is found by integration.
V=1.25t + 15.28
S = [pic]
S = [pic] + c
[pic]The displacement of Corolla is [pic]
However, when t = 0, S= 0.
Therefore C must equal zero.
[pic]The displacement of Corolla is