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Math Help - differenciation

  1. #1
    sss
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    differenciation

    A particle moves along a straight line and its position at time is given by where s is measured in feet and t in seconds.
    Find the velocity (in ft/sec) of the particle at time :
    The particle stops moving (i.e. is in a rest) twice, once when and again when where . is
    and is
    What is the position of the particle at time ?
    Finally, what is the TOTAL distance the particle travels between time and time ? ........how do we find the total distance???????
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sss View Post
    A particle moves along a straight line and its position at time is given by where s is measured in feet and t in seconds.
    Find the velocity (in ft/sec) of the particle at time :
    you want s'(0)

    the velocity function is the derivative of the position function
    The particle stops moving (i.e. is in a rest) twice, once when and again when where . is
    and is
    you want to solve v(t) = s'(t) = 0

    What is the position of the particle at time ?
    s(18)

    Finally, what is the TOTAL distance the particle travels between time and time ? ........how do we find the total distance???????
    if you have learned integrals, this is \int_0^{18} |v(t)|~dt
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    if you have learned integrals, this is \int_0^{18} |v(t)|~dt

    ...but what if you have not learned integrals; is there another way of approaching this problem?
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  4. #4
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    Quote Originally Posted by calculus shmalculus View Post
    ...but what if you have not learned integrals; is there another way of approaching this problem?
    total distance = [s(3) - s(0)] - [s(6) - s(3)] + [s(18) - s(6)]
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