The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are constants. At t = 0, the object is set in motion with velocity vo. Assume vo > 0. (a) Show that the object comes to rest in a finite time if and only if n < 1, and determine the maximum distance travelled by the object in this case. (b) If 1 < n < 2, show that the maximum dis- tance travelled by the object in a finite time is less than 2-n (2 – n)k
The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are constants. At t = 0, the object is set in motion with velocity vo. Assume vo > 0. (a) Show that the object comes to rest in a finite time if and only if n < 1, and determine the maximum distance travelled by the object in this case. (b) If 1 < n < 2, show that the maximum dis- tance travelled by the object in a finite time is less than 2-n (2 – n)k
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:The differential equation governing the velocity of an
object is
dv
-kv",
dt
where k > 0 and n are constants. At t = 0, the object
is set in motion with velocity vo. Assume vo > 0.
(a) Show that the object comes to rest in a finite time
if and only if n < 1, and determine the maximum
distance travelled by the object in this case.
(b) If 1 < n < 2, show that the maximum dis-
tance travelled by the object in a finite time is less
than
2-n
(2 – n)k
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