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?

Question

Mathematics

Evelyn

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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Answers (1)

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Kenyon Macias · Answer 1

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.