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    Find the distance travelled.

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    A particle moves along a line so that its velocity at time t is v(t)= t^2-t-6 m/s
    a) Find the displacement of the particle during the time period 2< or equal to t< or equal to 4
    and interpret the result.
    b) Find the distance traveled during this time period.

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    https://brainmass.com/math/basic-calculus/find-distance-traveled-287608

    Solution Preview

    A particle moves along a line so that its velocity at time t is v(t)= t2-t-6 m/s.

    a) Find the displacement of the particle during the time period 2 < t < 4
    and interpret the result.

    b) Find the distance travelled during this time period.

    Solution: Velocity v(t) = dx/dt = t2 - t - 6 ....... (1) where x represents the displacement of the particle.

    dx = (t2 - t - 6)dt

    Integrating we get: ∫dx = ∫(t2 - t - 6)dt

    Displacement x = t3/3 - t2/2 - 6t + C ...........(2) where C is the constant of integration

    Assuming at t = 0, x = 0. Substituting in (2) we get C = 0. ...

    Solution Summary

    The expert finds the distance traveled during this time period.

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