(a) True or false? The same curve can be described by parametric equations in many different ways. O True O False (b) The parametric equations x = 2t, y = (2t)2 model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation , which is the same as the equation for the path of an object with parametric equations x = t, y = 2, tz 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = and when t = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)2.)
(a) True or false? The same curve can be described by parametric equations in many different ways. O True O False (b) The parametric equations x = 2t, y = (2t)2 model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation , which is the same as the equation for the path of an object with parametric equations x = t, y = 2, tz 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = and when t = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)2.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) True or false? The same curve can be described by parametric equations in many different ways.
O True
False
(b) The parametric equations x = 2t, y = (2t)² model the position of a moving object at time t. When t =
0, the object is at
and when t = 1, the object is at
(c) If we eliminate the parameter, we get the equation
which is the same as the equation for the path of
object with parametric equations x = t, y = t², t> 0. So the two
objects move along the same path but traverse the path differently. Indicate the position of each object when t = 0 and whent = 1 on a graph. (Let A be the object whose motion is given by the
parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)².)
V
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