A particle moves along the x axis such that at time t (in seconds) the position

Question

A particle moves along the x axis such that at time t (in seconds) the position is given by S(t) = t^3 - 6t^2 + 9t + 11 feet. Find velocity at any time t. What is the velocity of the particle at t = 0 seconds? Find acceleration at any time t. What is the acceleration of the particle at t = 0 seconds? During what time Intervals is the particle moving left? Justify your answer. What is the total distance traveled by the particle from t = 0 to t = 2 seconds? What is the particle's displacement over the same time interval?

Explanation / Answer

c)particle will move left ewhen its velocity is -ve

hence velocity =3t2-12t+9<0

(3t2-9t-3t+9)<0

(3t(t-3)-(t-3)<0

(t-3)(3t-1)<0

which is -ve between -1/3<t<3

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