Calculus Project

A detailed Summary of Calculus Project


This new roller coaster, as you will see, has distinct problems at x= 100.5, 137.5 and 149.5. At these points the track is uneven and has gaps or bumps. For these to be dealt with, the dimensions(functions) provided to construct the coaster must be altered. This is done by splining(see Appendix-Definitions). The functions that are being splined, in addition to, their first and second derivatives must be known. The derivatives are taken to match the slope(first derivative)and concavity(second derivative) at a point where two functions meet. When those results don't match, the roller coaster isn't as smooth as it should be. This is where altering the current spline comes in handy. After the splines are corrected, the new track is operational, smooth and doesn't jerk as it did before. The roller coaster is now safe

Shown in the following appendix is an in depth, detailed analysis of the different problems associated to the coaster track and the repairs(splines) made to correct them.


matical term used to describe, in this case, the curve that joins two functions at the nearest end points. For example, when you want to join a loop to a straight line to construct a "loop the loop", a spline is made to connect them.

First Derivative-this term is used to find many factors, such as the slope of the tangent line to a curve, the velocity of a particle, and so on. As far as roller coasters are concerned, the first derivative is used to distinguish errors and the slope of the track.



Some common words found in the essay are:
Research Using, Definitions Spline-a, , roller coaster, potential energy, derivative derivative, roller coasters, top hill, kinetic energy, top hill energy, third derivative, energy function, coaster track, supply energy,

Approximate Word count = 685
Approximate Pages = 3 (250 words per page double spaced)

Category: Miscellaneous

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