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.
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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
Transcribed Image Text: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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