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  3. a particle moves along the xaxis such that its position...

Question: a particle moves along the xaxis such that its position...

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A particle moves along the x-axis such that its position is given by the function x(t) = t/4 - cos(t^2 / 3) and its velocity is given by the function v(t) = 1/4 + (2t/3)sin(t^2 / 3) for 0 <= t <= 5.

3. A particle moves along the x-axis such that its position is given by the function x(t) 1 2t t2 and its velocity is given by the function vt) sin for 0 t s5 a) Find the average velocity of the particle on the interval [0, 5]. b) When is the particle at the origin? c) When is the particle at rest? d) Identify the open interval or intervals when the particle is moving to the left. e) At time t 3, is the speed of the particle increasing or decreasing? Justify your answer.

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