The location P(t) of an object moving in the xy-plane at time t seconds is given by the equations P(t)=(x(t), y(t)), where x(t)=a +9t and y(t)=b +10t, a,b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review. (a) The location of the object at time t=1 is ( (b) The average rate of change of x(t) between 1 and 2 seconds is m/s. This is called the average horizontal velocity on the time interval [1,2]. (c) What is the instantaneous horizontal velocity of the object at time t? (d) The average rate of change of y(t) between 1 and 2 seconds is This is called the average vertical velocity on the time interval [1,2]. (e) What is the instantaneous vertical velocity of the object at time t? (f) The line along which the object is moving in the plane has the equation: y= x+ (g) Let d(t) be the distance the object has traveled after t seconds. d(t) = (h) The instantaneous rate of change of d(t) at time t is This is called the speed along the line of motion. m/s. Find parametric equations for the path of a particle that moves along the circle described by x² + (y-3)² = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 3). 0 sts 2π. (b) Three times around counterclockwise, starting at (4,3). O sts 6. (c) Halfway around counterclockwise, starting at (0, 7). O sts π.
The location P(t) of an object moving in the xy-plane at time t seconds is given by the equations P(t)=(x(t), y(t)), where x(t)=a +9t and y(t)=b +10t, a,b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review. (a) The location of the object at time t=1 is ( (b) The average rate of change of x(t) between 1 and 2 seconds is m/s. This is called the average horizontal velocity on the time interval [1,2]. (c) What is the instantaneous horizontal velocity of the object at time t? (d) The average rate of change of y(t) between 1 and 2 seconds is This is called the average vertical velocity on the time interval [1,2]. (e) What is the instantaneous vertical velocity of the object at time t? (f) The line along which the object is moving in the plane has the equation: y= x+ (g) Let d(t) be the distance the object has traveled after t seconds. d(t) = (h) The instantaneous rate of change of d(t) at time t is This is called the speed along the line of motion. m/s. Find parametric equations for the path of a particle that moves along the circle described by x² + (y-3)² = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 3). 0 sts 2π. (b) Three times around counterclockwise, starting at (4,3). O sts 6. (c) Halfway around counterclockwise, starting at (0, 7). O sts π.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 12T
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![The location P(t) of an object moving in the xy-plane at time t seconds is given by the equations P(t)=(x(t), y(t)), where x(t)=a +9t and y(t)=b +10t, a,b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review.
(a) The location of the object at time t=1 is (
(b) The average rate of change of x(t) between 1 and 2 seconds is
m/s.
This is called the average horizontal velocity on the time interval [1,2].
(c) What is the instantaneous horizontal velocity of the object at time t?
(d) The average rate of change of y(t) between 1 and 2 seconds is
This is called the average vertical velocity on the time interval [1,2].
(e) What is the instantaneous vertical velocity of the object at time t?
(f) The line along which the object is moving in the plane has the equation:
y=
x+
(g) Let d(t) be the distance the object has traveled after t seconds.
d(t) =
(h) The instantaneous rate of change of d(t) at time t is
This is called the speed along the line of motion.
m/s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5e3918c-0667-402f-8416-7840e886e6c8%2F0aa6a592-8aac-404f-8522-874100dbd3cc%2Fhhwjpy8_processed.png&w=3840&q=75)
Transcribed Image Text:The location P(t) of an object moving in the xy-plane at time t seconds is given by the equations P(t)=(x(t), y(t)), where x(t)=a +9t and y(t)=b +10t, a,b are constants and distances are measured in units of meters. The equations x(t), y(t) describe linear parametrized motion; see section 10.1 of the textbook for review.
(a) The location of the object at time t=1 is (
(b) The average rate of change of x(t) between 1 and 2 seconds is
m/s.
This is called the average horizontal velocity on the time interval [1,2].
(c) What is the instantaneous horizontal velocity of the object at time t?
(d) The average rate of change of y(t) between 1 and 2 seconds is
This is called the average vertical velocity on the time interval [1,2].
(e) What is the instantaneous vertical velocity of the object at time t?
(f) The line along which the object is moving in the plane has the equation:
y=
x+
(g) Let d(t) be the distance the object has traveled after t seconds.
d(t) =
(h) The instantaneous rate of change of d(t) at time t is
This is called the speed along the line of motion.
m/s.
Transcribed Image Text:Find parametric equations for the path of a particle that moves along the circle described by x² + (y-3)² = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.)
(a) Once around clockwise, starting at (4, 3). 0 sts 2π.
(b) Three times around counterclockwise, starting at (4,3). O sts 6.
(c) Halfway around counterclockwise, starting at (0, 7). O sts π.
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