0
$\begingroup$

Actually, this is the original question:

A particle moves along the x-axis so that the distance traveled in time $t$ is given by $x=2t + \cos 3t$. Find the distance between the first two positions of rest.

The ans given is 0.37 unit.

  • 2
    $2t+\cos\,3t=0$ is a transcendental equation; there isn't a general method to solve equations like these explicitly. One could use *numerical* methods for generating approximate solutions, though.2011-09-21
  • 0
    @J.M. I see, thanks a lot!2011-09-21
  • 3
    @J.M. We do not need to solve $x(t)=2t+\cos(3t)=0$ at all. We need to solve $v(t) = 0$, where $v(t)= x'(t)$ is the velocity. The roots are just arcsin of some number.2011-09-21
  • 2
    @Sri: I was addressing [revision 1](http://math.stackexchange.com/revisions/66358/1) of the question. Now I see OP edited to a different question. Not cool.2011-09-21
  • 1
    Not you, @Sri. You had no fault. It was the OP's bait-and-switch that had me bummed.2011-09-21
  • 1
    So @Sophia: Your initial translation of the problem was wrong. You need to solve $x'(t) = 0$ for the two smallest positive $t_1, t_2$ and then calculate the distance travelled between these two times, i.e. $x(t_2) - x(t_1)$.2011-09-21
  • 2
    @Sophia When you are editing a question, please do not edit it so substantially that it will invalidate a comment or answer. If such an edit is necessary, then **mention somewhere (either in the question itself or in the comments) that you have modified the question**. Otherwise different people will be seeing/solving different revisions of the question, leading to unnecessary confusion.2011-09-21
  • 0
    I found the solution already, thanks everyone.2011-09-22

2 Answers 2