kinematics

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these are two similar kinematics maths question which i don't know. Please help!

1)A particle moves in a straight line so that its distance, s metres, from a fixed point O is given by s = 2t^3 - 3t^2 - 12t + 6, where t is the time in seconds after passing O. Find the minimum speed attained by the particle

2)A particle moves in a straight line so that its distance, s meters, from a fixed point is given by s=t^3(2-t)^2, where t is the time in seconds after passing through the fixed point. What is the greatest distance travelled by the particle?

  • kinematics -

    Bailey, Andrea, Danny, Riley, anabelle, holly, LILLY, zachary, I'm stumped -- or whoever!

    To quote one of our very good math and science tutors: “You will find here at Jiskha that long series of questions, posted with no evidence of effort or thought by the person posting, will not be answered. We will gladly respond to your future questions in which your thoughts are included.”

  • kinematics -

    1) The speed at time t is
    |ds/dt| = |6t^2 -6t -12|
    (Speed is always positive)
    The minimum value of |ds/dt| is 0 if there is a time when
    6t^2 -6t -12 = 0
    t^2 -t -2 = 0
    (t-2)(t+1) = 0
    So there IS a time when the speed is zero.

    2) The greatest value of s occurs at a time where ds/dt = 0 is the second derivative d^2/dt^2 at that time is negative.

    s grows without bound for very large t greater than 2. I do not see how there could be a greatest value of s unless you restrict the region of consideration to 0 < t <2
    t = 2

  • kinematics -

    In my answer to 2), "is" should be "if".
    Sorry about that

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