A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 2t² - 4t and y = 3t² - 1³. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 2 s.

A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 2t² - 4t and y = 3t² - 1³. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 2 s.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

2/62 A particle which moves with curvilinear motion has
coordinates in millimeters which vary with the time t
in seconds according to x = 2t² - 4t and y = 3t² -
Determine the magnitudes of the velocity v and
acceleration a and the angles which these vectors
make with the x-axis when t = 2 s.
2/62
x = 2t²-4t
y = 3t² - +³
y = 6t-t²
x=4t - 4
**
x = 4 mm/s²
y
= 6-2t
At t=2s: x = 4(2)-4
= 4mm/s
(y
=
= 6(2)-2². = 8 mm/s
√= √√x ² + y² =
T
√4²+8²= 8.94 mm/s
63.4'
At t = 25:
x = 4 mm/s²
ÿ = 6-2(2) = 2mm/s²
√√4² +2²= 4.47 mm/s ²
√√4² +2²
a =
0x = tan".
= tan¹ ² = 26.6°
= tan¹ = tan ¹
√√²+ÿ² =
solf

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