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Two particles 1 and 2 move along + -axis such that 2 is ahead of 1 by 4m both on the right side of the origin.The velocity of 1 is directly proportional to the position of 2, and the velocity of 2 is directly proportional to the position of 1, the proportionality constant being the same, equal to . Find the time in seconds after which their separation becomes .
The answer is 2.
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1 solution
Well...someone has to write it I guess? Evaluate xrel, which is the difference between x2 and x1: it will be equal to the integral of the natural logarithm of 2 times the opposite of x rel with respect to time (this follows from subtracting their velocities). Now we can derive both members of the equation as xrel is a function of time, then separating the d(xrel) from dt and integrating from 4m to 1m will give the answer ( t goes from 0 to the time T which we want to find). I'm sorry but I can't use Latex and wanted to avoid writing formulas as much as possible, I will try to answer every question about the problem.