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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ElleNicocobe ElleNicocobe

20-07-2016
Mathematics

contestada

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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meerkat18 meerkat18 · Answer 1 · 2016-07-20T17:59:08+02:00

meerkat18 meerkat18

20-07-2016

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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