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calculus

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The velocity function is v(t) = - t^2 + 4 t - 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].

  • calculus - ,

    displacement = integral v dt
    = -t^3/3 + 2 t^2 - 3 t
    from -2 to +6
    do the arithmetic

    distance traveled
    that means always use absolute value of any part of the integral
    when is velocity negative and when is it positive?
    0 = t^2 - 4 t + 3
    0 = (t-3)(t-1)
    velocity 0 at t = 1 and t = 3
    so:
    take absolute value of integral from
    -2 to + 1
    add to absolute value of integral from +1 to +3
    add to absolute value of integral from +3 to + 6

  • calculus - ,

    thank you

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