A particle moves along the x-axis so that its velocity at time t is given by v(t) = ((t^6)-(13t^4)+(12)) / ((10t^3)+3) At time t = 0, the initial position of the particle is x = 7. (a) Find the acceleration of the particle at time t = 5.1. (b) Find all values of t in the interval 0 (less than or equal to) t (less than or equal to) 2 for which the speed of the particle is 1. (c) Find the position of the particle at time t = 4. Is the particle moving toward the origin or away from the origin at time t = 4 ? Justify your answer (d) During the time interval 0 < t (less than or equal to) 4, does the particle return to its initial position? Give a reason for your answer.
A particle moves along the x-axis so that its velocity at time t is given by v(t) = ((t^6)-(13t^4)+(12)) / ((10t^3)+3) At time t = 0, the initial position of the particle is x = 7.
(a) Find the acceleration of the particle at time t = 5.1.
(b) Find all values of t in the interval 0 (less than or equal to) t (less than or equal to) 2 for which the speed of the particle is 1.
(c) Find the position of the particle at time t = 4. Is the particle moving toward the origin or away from the origin at time t = 4 ? Justify your answer
(d) During the time interval 0 < t (less than or equal to) 4, does the particle return to its initial position? Give a reason for your answer.
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