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rsala

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## Homework Statement

A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the x-axis be parallel to the ground and the positive y-axis point upward. In the time interval from t=0 to t=4 s, the trajectory of the car along a certain section of the track is given byhttp://img526.imageshack.us/img526/719/renderxg2.gif

__where A is a positive dimensionless constant.__

The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding 20m/s.

The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding 20m/s.

__Find the maximum value of A allowed by these regulations.__## Homework Equations

A = [tex]\sqrt{a_{x}^{2} + a_{y}^{2}}[/tex]

## The Attempt at a Solution

well, I have separated this equation into 2 components of position, rx ry

Rx = A(t)

Ry= A(T[tex]^{3}[/tex] - 6T[tex]^{2}[/tex])

took the derivative of each component to change R to V

Vx = A (this is A because, A is a constant and i just treated this as i took the deriative of any constant next to a variable with power of 1, just kept the constant.)

Vy = A(3T[tex]^{2}[/tex] - 12T)

The magnitude of this vector V is

V = [tex]\sqrt{ A^{2} + (3T^{2}-A12T)^{2}}[/tex]now.. my problem here is how can i find which maximum value of A whose speed doesn't pass 20, i HAVE thought of setting this equation to 20, but what about -20 velocity, since it asks for speed not velocity...this rollercoaster CAN go downward.

any advice?

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