I am trying to find the average velocity of s(t) = cost(sqrt(13+8sint) during the period 0
can someone please help me or explain how to start?
should I use integral?
should I use integral?
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The average velocity is ∆s/∆t = [s(π) - s(0)]]/π
s(π) = cos(π*(√[13 8*sin(π)])
sin(π) = 0
s(π) = cos(π*√[13]) = 0.326
s(0) = cos(0) = 1
∆s = -0.674
Vav = -0.674/π = -0.21
s(π) = cos(π*(√[13 8*sin(π)])
sin(π) = 0
s(π) = cos(π*√[13]) = 0.326
s(0) = cos(0) = 1
∆s = -0.674
Vav = -0.674/π = -0.21
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No calculus is required.
I'll use: s(t) = [cos(t)] [sqrt(13+8sin(t)]
The initial position, when t=0, is s(0):
s(0) = [cos(0)] [sqrt(13+8sin(0)]
= [1] [sqrt(13)]
= sqrt(13)
The final position, when t = pi, is s(pi):
s(pi) = [cos(pi)] [sqrt(13+8sin(pi)]
= [-1] [sqrt(13)]
= - sqrt(13)
Average velocity = resultant displacement / time
= [final position - initial position] / time
= [s(pi) - s(0)] / (pi - 0)
= [-sqrt(13) - sqrt(13)] / pi
= -2sqrt(13)/pi
I'll use: s(t) = [cos(t)] [sqrt(13+8sin(t)]
The initial position, when t=0, is s(0):
s(0) = [cos(0)] [sqrt(13+8sin(0)]
= [1] [sqrt(13)]
= sqrt(13)
The final position, when t = pi, is s(pi):
s(pi) = [cos(pi)] [sqrt(13+8sin(pi)]
= [-1] [sqrt(13)]
= - sqrt(13)
Average velocity = resultant displacement / time
= [final position - initial position] / time
= [s(pi) - s(0)] / (pi - 0)
= [-sqrt(13) - sqrt(13)] / pi
= -2sqrt(13)/pi