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Math Help - average velocity

  1. #1
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    average velocity

    Consider a car whose position, s, is given by the table

    t (sec) 0 0.2 0.4 0.6 0.8 1
    s (ft) 0 0.5 1.7 3.8 6.5 9.6

    Find the average velocity over the interval 0<=t<=0.2

    Estimate the velocity at t=0.2
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  2. #2
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    Velocity is calculated as distance over time, so the average velocity over an interval will be the total distance traveled in that interval divided by the total time taken to travel that distance.
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  3. #3
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    ok that makes sense but how do you estimate the time at 0.2?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cwarzecha View Post
    Consider a car whose position, s, is given by the table

    t (sec) 0 0.2 0.4 0.6 0.8 1
    s (ft) 0 0.5 1.7 3.8 6.5 9.6

    Estimate the velocity at t=0.2
    Sketch a graph of the data then sketch a smooth curve connecting those points. The instantaneous speed at 0.2 s will be the slope of the line that is tangent to your curve at 0.2 s.

    -Dan
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  5. #5
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    i sketched a graph and i got a line. is it the slope of that line?
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cwarzecha View Post
    i sketched a graph and i got a line. is it the slope of that line?
    Yes, the slope of the line tangent to a given line is the slope of the given line.

    Ie. The slope of the tangent to y = mx + b is m.

    -Dan
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