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Math Help - Motion along a straight line question

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    Motion along a straight line question

    A particle moves from fixed pt. O along a straight line. It's velocity v m/s, t s after passing through O is given by v=4t-5. Find the total distance traveled by the particle when t=3. The answer is 48.25m. Any help? This book has lots of error-ed answers, so I'm not really sure..
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  2. #2
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    Quote Originally Posted by smmxwell View Post
    A particle moves from fixed pt. O along a straight line. It's velocity v m/s, t s after passing through O is given by v=4t-5. Find the total distance traveled by the particle when t=3. The answer is 48.25m. Any help? This book has lots of error-ed answers, so I'm not really sure..
    I do not agree with the "answer". assuming that the question is asking for total distance traveled from t = 0 to t = 3 ...



    particle is moving left from t = 0 to t = 5/4 sec

    distance traveled in that interval = (1/2)(5/4)(5) = 25/8 m


    from t = 5/4 to t = 3 sec, the particle moves to the right ...

    distance traveled in that interval = (1/2)(7/4)(7) = 48/8 m


    total distance traveled = 25/8 + 49/8 = 74/8 = 9.25 m



    total distance can also can be calculated by the definite integral ...

    \int_0^3 |4t-5| \, dt
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  3. #3
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    Thanks. Guess my anwser was correct all along.
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