math(mechanics)

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the velocity of a particle traveling in a straight line is given by v=(6t-3t^2)m/s, where t is in seconds, if s=0 when t= 0. determine the particles deceleration and position when t=3s. how far has the particle traveled during the 3s time interval and what is its average speed?

  • math(mechanics) -

    if v = 6t - 3t^2
    then a = 6 - 6t
    and s = distance = 3t^2 - t^3 + c , where c is a constant.
    but we are told that s-0 when t= 0 , so c = 0

    when t = 3
    a = 6 - 6(3) = - -12
    s = 3(3^2) - 3^3 = 0

    total distance = final position - initial position
    = 0 - 0 = 0
    avg speed = 0/3 = 0

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