- #1
desquee
- 18
- 1
This was given as a problem in a calculus textbook I'm working through (apologies if this should have gone in the physics forum)
1. Homework Statement
An ant crawls at 1foot/second along a rubber band whose
original length is 2 feet. The band is being stretched at 1
foot/second by pulling the other end. At what time T, if ever,
does the ant reach the other end?
One approach: The band's length at time t is t + 2. Let y(t)
be the fraction of that length which the ant has covered, and
explain
(a) y' = 1/(t + 2) (b)y =ln(t + 2) -ln 2 (c) T = 2e -2.
∫1/x dx = ln(x)
Given a, I can get to b by integrating and finding the constant, and then to c by solving for y=1, but I'm stumped on how to get to explain a. y' seems to be the ant's speed over the length of the band, by I don't understand why that is so.
1. Homework Statement
An ant crawls at 1foot/second along a rubber band whose
original length is 2 feet. The band is being stretched at 1
foot/second by pulling the other end. At what time T, if ever,
does the ant reach the other end?
One approach: The band's length at time t is t + 2. Let y(t)
be the fraction of that length which the ant has covered, and
explain
(a) y' = 1/(t + 2) (b)y =ln(t + 2) -ln 2 (c) T = 2e -2.
Homework Equations
∫1/x dx = ln(x)
The Attempt at a Solution
Given a, I can get to b by integrating and finding the constant, and then to c by solving for y=1, but I'm stumped on how to get to explain a. y' seems to be the ant's speed over the length of the band, by I don't understand why that is so.