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Velocity rate question

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data
    s(t)= Vit + 1/2 a t^2 + So

    a) find the average velocity on the interval [1,3]
    b) find the instantaneous velocity when t= 3s.
    c) how long does it take the coin to hit the ground?
    d) find the velocity when the coin hits the ground


    2. Relevant equations
    a= -32ft/(s^2)


    3. The attempt at a solution
    S(t)=Vi(0)t + 1/2 (-32ft/s^2)t^2 +So
    S(t)= 0 -16t^2 + 800
    v(t) = -32t

    a) V(3)-V(1)/(3-1)
    V(3) = -32(3)=-96
    V(1) = -32(1)= -32

    -96-(-32)/2 = -64ft/sec is my final answer

    b) v(3)= -32(3)

    C)coin hits ground at s(t)= 0 S(t)= -16t^2 + 800
    0= =16t^2 +800
    -800= -16t^2
    sqr50= t^2
    7.071 seconds is when the coin hits the ground
    D) V(t) =-32t
    V(7.071)= -32(7.071)
    v= -226.272 ft/sec
     
  2. jcsd
  3. Nov 11, 2012 #2
    1) Yes the average velocity can be calculated by differentiating s(t)
    ∴ s(t[itex]^{'}[/itex]) = -32t
    The average velocity turns out to be (-96 + 32)/2 = -32

    2) The instantaneous velocity when t=3 s is given by
    Lim Δt→0 Δs/Δt = ds/dt
    So -32t = -32 × 3 = -96

    3) s(t[itex]^{'}[/itex]) = -32t
    ∴ s(t) = [itex]\int[/itex] -32t dt
    = -16t[itex]^{2}[/itex] + C

    4) Velocity is zero as when t=0 ; -32t = -32 × 0 = 0
     
  4. Nov 11, 2012 #3

    haruspex

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    There seem to be other facts which you introduce later. From those I infer a coin is dropped from rest at time 0 and a height of 800ft.
    No, that will give you the average of two specific speeds. That is not the same as the average speed over an interval. Average speed = change in distance / change in time.
    Abhinav R's method and answer are wrong too.
     
  5. Nov 12, 2012 #4
    How do I do it then if the methods are wrong?
     
  6. Nov 12, 2012 #5

    SammyS

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    Please state the complete problem as it was given to you.
     
  7. Nov 12, 2012 #6

    haruspex

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    As I said, Average speed = change in distance / change in time. Where was it at t=1? Where at t=3? How far did it travel between t=1 and t=3?
     
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