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Math Help - Distance and Displacement Question

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    Distance and Displacement Question

    The velocity function is for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,6].

    displacement = distance traveled =

    OK so I found the displacement which is -12, but I can't find the distance. I know I have to find when it changes directions and I found it did that at x=3. Can someone help? Thanks
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    Quote Originally Posted by softballchick View Post
    The velocity function is for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,6].

    displacement = distance traveled =

    OK so I found the displacement which is -12, but I can't find the distance. I know I have to find when it changes directions and I found it did that at x=3. Can someone help? Thanks
    Assuming that your v(t) is a velocity, then you have got it right:
    \displaystyle \vec{s(t)} = \int_0^6 v(t) dt

    To find a distance, which is the magnitude of the velocity:
    \displaystyle s(t) = \int_0^6 |v(t)| dt

    where |v(t)| is the magnitude of the velocity, in this case the absolute value of the velocity function. Here are the two relevant graphs.

    -Dan
    Attached Thumbnails Attached Thumbnails Distance and Displacement Question-distance.jpg   Distance and Displacement Question-displacement.jpg  
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