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20 May, 14:27

A particle moves along the x-axis so that its position at any time t> 0 is given by x (t) = t^4 - 10t^3 + 29t^2 - 36t + 2. For which value of t is the speed the greatest?

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  1. 20 May, 16:14
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    Speed is the derivative of distance, x (t), with respect to time.

    speed = dx/dt = 4t³ - 30t² + 58t - 36

    The time at which the speed is greatest is the derivative of the speed equated to zero.

    ds/dt = 12t² - 60t + 58 = 0

    The value of t from the equation are 3.69 and 1.31 seconds.
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