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anonymous
 one year ago
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
anonymous
 one year ago
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

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2you can find the position function by integrating the velocity function and then apply the condition s(0)=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you can find the average velocity over the interval t in [0,8] by computing: \[\frac{s(8)s(0)}{80}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0acceleration >integrate > velocity velocity > integrate > displacement

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the average velocity be 3.33

phi
 one year ago
Best ResponseYou've already chosen the best response.0oh wait. first subtract off s(0)= 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.2can you find the instantaneous velocity? (hint: think derivative of position)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and you are actually already given the derivative of the position :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0instantantaneous velocity is dx/dt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you plug in 5 into the v(t)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2are you sure @phi that is what I got

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do I find the average velocity with initial condition s(0)=1

phi
 one year ago
Best ResponseYou've already chosen the best response.0oh, never mind. that constant is subtracted off. so yes 3.333

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can always check your answer on wolframalpha, but phi has a good explanation on it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you very much!

phi
 one year ago
Best ResponseYou've already chosen the best response.0how 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 80= 8
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