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Math Help - instantenous motion

  1. #1
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    Smile instantenous motion

    Guys as always I appreciate you help. I think this is one of the best sites on the internet. I do however have a question:

    A particle moves along a straight line and its position at time t s given by s(t)= 2t^3 - 15 t^2 + 24 t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t=0___?___. The particle stops moving twice, once when t=A and again when t=B where A<B. A is ___?____
    & B is ___?___. What is the position of the particle at time 10 ___?____.


    Thanks Again!
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  2. #2
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    Quote Originally Posted by qbkr21 View Post
    Guys as always I appreciate you help. I think this is one of the best sites on the internet. I do however have a question:

    A particle moves along a straight line and its position at time t s given by s(t)= 2t^3 - 15 t^2 + 24 t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t=0___?___. The particle stops moving twice, once when t=A and again when t=B where A<B. A is ___?____
    & B is ___?___. What is the position of the particle at time 10 ___?____.


    Thanks Again!
    It's velocity is ds/dt = 6 t^2 -30 t +24, so at t=0 ds/dt=24 ft/s.

    The particle stops moving when ds/dt=0, but:

    ds/dt = 6 t^2 -30 t +24 = (t-1)(6t-24)

    so ds/dt = 0, when t=1 s, and again when t=4 s, so A=1, and B=4.

    Now s(t)= 2t^3 - 15 t^2 + 24 t, so at t=10:

    s(10) = 2*1000 - 15*100 + 24*10 = 740 ft.

    RonL
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