The velocity of a given object is determined by -kv", k >> 0, n 2 0 a constant. (This is often used when examining air resistance, but do try to figure out where the method fails.) At t 0, the object is moving with a positive initial velocity of vo and continues until its velocity reaches zero (if it ever does) (a) Show that the object comes to a rest in a finite amount of time if and only if n < 1 and find the maximum distance travelled in this case (b If 1 n2, show that the maximum distance travelled by the object in a finite time is less than (vo2-)/[(2- n)k]. (c) Show that if n 2 2, then there is no limit to the distance the object can travel

The velocity of a given object is determined by -kv", k >> 0, n 2 0 a constant. (This is often used when examining air resistance, but do try to figure out where the method fails.) At t 0, the object is moving with a positive initial velocity of vo and continues until its velocity reaches zero (if it ever does) (a) Show that the object comes to a rest in a finite amount of time if and only if n < 1 and find the maximum distance travelled in this case (b If 1 n2, show that the maximum distance travelled by the object in a finite time is less than (vo2-)/[(2- n)k]. (c) Show that if n 2 2, then there is no limit to the distance the object can travel

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

The velocity of a given object is determined by -kv", k >> 0, n 2 0 a constant. (This is
often used when examining air resistance, but do try to figure out where the method fails.) At
t 0, the object is moving with a positive initial velocity of vo and continues until its velocity
reaches zero (if it ever does)
(a) Show that the object comes to a rest in a finite amount of time if and only if n < 1 and find
the maximum distance travelled in this case
(b If 1 n2, show that the maximum distance travelled by the object in a finite time is less
than (vo2-)/[(2- n)k].
(c) Show that if n 2 2, then there is no limit to the distance the object can travel

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