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Math Help - position function help!

  1. #1
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    position function help!

    A particle moves according to the position function
    f(t)=sin(pi(t)/4) , t>or equal to 0 , t in seconds, s in feet.

    a. find the average velocity of the particle over the interval [1,5]
    b. when is the particle at rest in the first 10 seconds?
    c. Find the total distance traveled during the first 10 seconds by drawing a path of the motion.

    Thank you!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by olemiss13 View Post
    A particle moves according to the position function
    f(t)=sin(pi(t)/4) , t>or equal to 0 , t in seconds, s in feet.

    a. find the average velocity of the particle over the interval [1,5]
    b. when is the particle at rest in the first 10 seconds?
    c. Find the total distance traveled during the first 10 seconds by drawing a path of the motion.

    Thank you!!
    First note that the velocity function is given by v(t) = f'(t)

    For (a): Average velocity on [1,5] = \frac {f(5) - f(1)}{5 - 1}

    For (b): You want v(t) = 0, and solve for the t values between 0 and 10

    For (c): Distance traveled in the first 10 seconds = \int_0^{10} |v(t)|~dt
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