Parametric Equations and And a Parameter Interval for the Motion $x=4 t^{2}, y=2 t, x \leq t \leq \infty$

question 191

Multiple Choice

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
- $x=4 t^{2}, y=2 t, x \leq t \leq \infty$

• A) \(x = y ^ { 2 }\); Entire parabola, top to bottom (from1st quadrant to origin to 2nd quadrant)
• B) \(y = x ^ { 2 }\); Entire parabola, right to left (from 1st quadrant to origin to 4 th quadrant)
• C) \(x = y ^ { 2 }\); Entire parabola, bottom to top (from 2nd quadrant to origin to 1st quadrant)
• D) \(y = x ^ { 2 }\); Entire parabola, left to right (from 4th quadrant to origin to 1st quadrant)

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Definitions:

Good Theory

A well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation.

Operational Definition

A clear, precise way of defining a concept by specifying the operations or procedures used to measure or identify it.

Variable

An element, feature, or factor that is likely to vary or change in value between different individuals or under different conditions.

Scientific Method

A systematic and logical approach to discovering how things in the universe work, involving observation, experimentation, and hypothesis testing.