anonymous
  • anonymous
A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero, that is, s(0) = 1. 1.The average velocity over the interval 0 to 8 seconds 2.The instantaneous velocity and speed at time 5 secs Help please
Mathematics
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
you can find the position function by integrating the velocity function and then apply the condition s(0)=1
freckles
  • freckles
you can find the average velocity over the interval t in [0,8] by computing: \[\frac{s(8)-s(0)}{8-0}\]
anonymous
  • anonymous
acceleration ->integrate -> velocity velocity -> integrate -> displacement

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anonymous
  • anonymous
would the average velocity be 3.33
phi
  • phi
oh wait. first subtract off s(0)= 1
freckles
  • freckles
can you find the instantaneous velocity? (hint: think derivative of position)
freckles
  • freckles
and you are actually already given the derivative of the position :)
anonymous
  • anonymous
instantantaneous velocity is dx/dt
anonymous
  • anonymous
so you plug in 5 into the v(t)?
freckles
  • freckles
yep
freckles
  • freckles
are you sure @phi that is what I got
anonymous
  • anonymous
how do I find the average velocity with initial condition s(0)=1
freckles
  • freckles
http://www.wolframalpha.com/input/?i=1%2F8*%28%288%5E3%2F3-9%2F2%288%29%5E2%2B18%288%29%2B1%29-%281%29%29
phi
  • phi
oh, never mind. that constant is subtracted off. so yes 3.333
anonymous
  • anonymous
you can always check your answer on wolframalpha, but phi has a good explanation on it
anonymous
  • anonymous
thank you very much!
phi
  • phi
how do I find the average velocity with initial condition s(0)=1 after integrating v(t) you get \[ \frac{t^3}{3}- \frac{9t^2}{2} +18t + C \] when t is 0 that should be 1, i.e. C= 1 and when we do s(8)- s(0) the one's cancel. so we just need \[ \frac{t^3}{3}- \frac{9t^2}{2} +18t\] evaluated at t= 8 (for the top) the bottom is 8-0= 8

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