Particle P moves along the y-axis so that its position at time t is given by y (t) = 4t - for all times t. A second particle, particle Q, moves along the x-axis so that its position at time t is given by x (t) sin(at) = for all times t# 2. 2-t (a) As time t approaches 2, what is the limit of the position of particle Q? Show the work that leads to your answer. B I U X² X₂ Ć 22 (b) Show that the velocity of particle Q is given by vo (t) BIUX² X₂ C 22 E 111 M 2n cos(nt)-nt cos(at)+sin(at) (2-t)² for all times t 2. 0/10000 Word Lin 0/10000 W (c) Find the rate of change of the distance between particle P and particle Q at time t = Show the work that leads to your answer.
Particle P moves along the y-axis so that its position at time t is given by y (t) = 4t - for all times t. A second particle, particle Q, moves along the x-axis so that its position at time t is given by x (t) sin(at) = for all times t# 2. 2-t (a) As time t approaches 2, what is the limit of the position of particle Q? Show the work that leads to your answer. B I U X² X₂ Ć 22 (b) Show that the velocity of particle Q is given by vo (t) BIUX² X₂ C 22 E 111 M 2n cos(nt)-nt cos(at)+sin(at) (2-t)² for all times t 2. 0/10000 Word Lin 0/10000 W (c) Find the rate of change of the distance between particle P and particle Q at time t = Show the work that leads to your answer.
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:Particle P moves along the y-axis so that its position at time t is given by y (t) = 4t - for all times t. A second particle, particle Q, moves along
the x-axis so that its position at time t is given by x (t)
sin(at)
2-t
for all times t 2.
(a) As time t approaches 2, what is the limit of the position of particle Q? Show the work that leads to your answer.
X2 0
BIU x²x₂ 5
C C Ω
BIU X² X₂
=
!!!
3 C 2
FNM
(b) Show that the velocity of particle Q is given by vo (t)
!!!
|||
E
=
123
|||
2π cos(πt)-nt cos(nt)+sin(t)
12
(2-t)²
8 of 8
for all times t# 2.
0/10000 Word Lir
0/10000 W
(c) Find the rate of change of the distance between particle P and particle at time t = 1. Show the work that leads to your answer.
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