# The velocity function of a moving particle on a coordinate line is v(t) = 3 cos(2t)  for 0 is less than or equal     to t and t is greater than or equal to 2pi (c) Determine the distance travelled by the particle during 0 is less than or equal to t is greater than or equal to 2pi.

If you need to find the displacement of moving particle, under the given conditions, you need to evaluate the definite integral of the given function such that:

`s(t) = int_0^(2pi) 3cos 2t dt `

You need to come up with the following substitution such that:

`2t = u => 2dt =...

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If you need to find the displacement of moving particle, under the given conditions, you need to evaluate the definite integral of the given function such that:

`s(t) = int_0^(2pi) 3cos 2t dt `

You need to come up with the following substitution such that:

`2t = u => 2dt = du => dt = (du)/2`

`{(t = 0 => u = 0 ),(t = 2pi => u = 4pi ):}`

Changing the variable yields:

`int_0^(2pi) 3cos 2t dt = int_0^(4pi) 3cosu(du)/2`

`(3/2) int_0^(4pi) cos u du = (3/2) sin u|_0^(4pi)`

Using the fundamental theorem of calculus yields:

`(3/2) int_0^(4pi) cos u du = (3/2)(sin 4pi - sin 0) = 0`

Hence, evaluating the distance travelled by the moving particle yields `s(t) = 0.`

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