The position of a particle is given by r = (at2)i + (bt3)j + (ct-2)k, where...

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Question

The position of a particle is given by r = (at²)i + (bt³)j + (ct^-2)k, where a, b, and c are constants.

a) What is the velocity as a function of time?

b) What is the acceleration as a function of time?

c) Suppose a = 4.48 m/s², b = -2.63 m/s³, and c = -82.7 ms². What is the particle’s speed, in m/s, at t = 2.46 s?

d) Referring to the values given in part (c), what is the magnitude of the particle’s acceleration, in m/s², at t = 2.46 s?

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