Deriving s(t) from a x-y plane

Thread starter Phys_Boi
Start date Jan 19, 2016
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deriving Plane

AI Thread Summary

To find the position function s(t) from a table of time intervals, one must integrate the velocity function v(t), which can be derived from the given function f(x) = -x^2. The velocity v(t) is the first derivative of the position function, while acceleration a(t) is the second derivative. The relationship between these functions is crucial for understanding motion along the graph represented by f(x). Therefore, to determine s(t), one needs to establish v(t) first, then integrate to find the position over time. Understanding these derivatives and their relationships is essential for analyzing the particle's motion on the coordinate plane.

Jan 19, 2016

Phys_Boi

So if I'm given a coordinate plane that graphs the position of a particle, how do you get the s(t), in respect to time if given a table of time intervals.

Given:
f(x) = -x^2

Needed:
s(t)?
v(t)?
a(t)?

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Jan 20, 2016

Svein

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f(x) is an equation for the shape of the road. How fast you drive along that road is and entirely different question.

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