SOLUTION: The velocity of a particle is given by: v=1/(4cos2x) and initially the particle is at the origin. Find the total time of motion. I do not understand why the answer is 2.

Algebra ->  Expressions -> SOLUTION: The velocity of a particle is given by: v=1/(4cos2x) and initially the particle is at the origin. Find the total time of motion. I do not understand why the answer is 2.      Log On


   

Question 1142810: The velocity of a particle is given by: v=1/(4cos2x) and initially the particle is at the origin. Find the total time of motion.
I do not understand why the answer is 2.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Given a function f(x), df/dx is the rate of change of f. It is "velocity" only if f(x) is a position function that df/dx is the rate of change of position so "speed" or "velocity".
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v = 1/(4cos2x)
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therefore, v = dx/dt
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dx/dt = 1/(4cos2x)
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cos(2x) dx = dt/4
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integrate both sides
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t = 2 * sin(2x) +constant
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Note integral of cos(2x) = (1/2) * sin(2x) +constant
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initial condition is t=0, x=0
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constant = 0
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t = 2 * sin(2x)
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Now, what does "total time of motion" mean?
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