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A sonic ranger monitors a cart that moves along a track, monitoring with audible clicks that...

A sonic ranger monitors a cart that moves along a track, monitoring with audible clicks that occur every 13 ms. A computer analyzes the data obtained and gives a best fit function of:

x(t) = 0.00051 m/s t + 0.00015 m/s2 t2 - 5.4e-06 m/s3 t3

(a) At what time does the cart reach its farthest distance from the first sensor?


(b) How far from the first sensor does this happen?


(c) What is the acceleration at that spot?

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