# What is the average velocity of the particle from t = pi/3 to t = 7pi/3? Given: At time t in seconds, a particle's distance s(t), in centimeters, from a point is given by s(t) = 4 + 3 sin t.  What is the average velocity of the particle from t = pi/3 to t = 7pi/3? The distance s(t) is given by,

`s(t) = 4+3sin(t)`

The average velocity can be found according to following expression,

Average velocity = (Final distance - Initial distance)/Time

Distance at `t = pi/3`

`s(pi/3) = 4+3sin(pi/3) = 4+3(sqrt(3)/2)`

`s(pi/3) =` 6.598 cm

Distance at  `t = (7pi)/3`

`s(pi/3) = 4+3sin((7pi)/3)...

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The distance s(t) is given by,

`s(t) = 4+3sin(t)`

The average velocity can be found according to following expression,

Average velocity = (Final distance - Initial distance)/Time

Distance at `t = pi/3`

`s(pi/3) = 4+3sin(pi/3) = 4+3(sqrt(3)/2)`

`s(pi/3) =` 6.598 cm

Distance at  `t = (7pi)/3`

`s(pi/3) = 4+3sin((7pi)/3) = 4+3sin(2pi +(7pi)/3) = 4+3sin((pi)/3)`

s((7pi)/3) = 6.598 cm

Therefore,

Average velocity = (6.598 - 6.598)/(7pi/3 - pi/3)

= 0 `cms^(-1)`

The average velocity is 0 cm/s

Approved by eNotes Editorial Team