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The position of a dragonfly that is flying parallel to the ground is given as a function of time by r = [2.90+(0.0900^{2} )t^{2} ]i - (0.0150^{3} )t^{3} j.

At what value of t does the velocity vector of the insect make an angle of 38.0 ^{} clockwise from the *x*-axis?

At the time calculated in part (a), what is the magnitude of the acceleration vector of the insect?

At the time calculated in part (a), what is the direction of the acceleration vector of the insect?

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