ksaimouli
The position of a particle moving along a line is given by
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ksaimouli
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\[s(t)=2t^3-24t^2+90t+7\]
ksaimouli
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for what values t is the speed of particle increasing
Jonask
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\[s'(t) \implies velocity \space \space s''(t) \implies acceleration\]
ksaimouli
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ya i got a(t)=0 i got 4
ksaimouli
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as critical point
ceb105
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ds/dt=6t^2-48t+90
thus
d^2s/dt^2=12t-48 => aceleration is greater than zero when t>4
Jonask
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well first get the turning point,
you mean s'(t)=0
ksaimouli
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no i mean s''(t) gives acceleration =0 will give us information about velocity
Jonask
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yes so you got 4 right
ksaimouli
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yes
ceb105
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So yea it is when t>4 that the acceleration is postivei .e. speed increases
Jonask
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yes
ksaimouli
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no that not the answer i am looking for
ceb105
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Well its the right one...
ksaimouli
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but the answer is 3<t<4 and t>5 ( i was shocked !!!!
ceb105
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is it possible that this is wrong?
ksaimouli
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@hartnn
Jonask
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|dw:1360515901447:dw|
graph increasing
the speed inceases when the grapg rises so x<a and x>b
ceb105
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Okay well 3 and 5 are the critical points of the velocity
Jonask
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|dw:1360516136831:dw|
Jonask
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|dw:1360516160914:dw|
ksaimouli
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But why i need the critical points of velocity when they ask for velocity
ksaimouli
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This is no calculator question so i cannot graph
Jonask
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they did not say the rate of change in velocity nor speed just velocity increasing
Jonask
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yeah i know what i am saying is\[s'(t)=0\]
ksaimouli
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i e 0,3,5
ksaimouli
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then how did they get 4
Jonask
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so you get 3 and 5 right
ksaimouli
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yes
Jonask
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speed =|velocity|
\[|6t^2-8t+15|>0\]
i would like to explain grapghically 4 a sec
Jonask
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i mean\[|t^2-8t+15|\]
ksaimouli
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its actually velocity=I speedI
ksaimouli
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velocity is vector where as speed is scalar
Jonask
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i agree with person 3
ksaimouli
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i found out that they used velocity and acceleration derivatives and they set them =0 and found the answer but i have learned that to find graph of y' use y'' to find max or min
Jonask
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yes so we found \[|t^2-8t+15|>0 \implies t<3 ,t>5\]
but also for - velocity we put
\[-(t^2-8t+15)\]
its positive for
\[-(2t-8)>0 \implies t<4\]
(3,4) and x>5
Jonask
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did the link help