A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0?

Question

Question options:

1)	1
2)	2
3)	3
4)	More than 3

Answer 1

Hi Crystal F.,

So what do you need to do to get velocity from position? If your answer is, differentiate once with respect to time, you are right (so far!).

So -- how do you differentiate exp(cos(x)) with respect to t? Answer: you don't. Somewhere in there, someone messed around with a variable; I think what is intended is s(t) = exp (cos(t) ) ? [Else, you don't have any logical connect between s and t! And s can't be a function of itself! ]

Now (assuming you take that correction!) you have a differentiable form. Result d(s)/dt = exp (cos(t)) * (-sin(t)). If you want that to equal 0 , only one of the terms of that product can do that. Which one? And once you know that, you can cherry-pick the velocity-zero positions from the t (axis) for the sin function.

--Cheers, -- Mr. d.