(i) Sketch:

car racetrack

Note the axes are x- and y-based, and do not involve t.

(ii) Acceleration:

Horizontal acceleration:

x = 20 + 0.2t3



At t = 3.0, ax = 3.6

Vertical acceleration:

y = 20t − 2t2



At t = 3.0, ay = -4




`theta_a=arctan((a_y)/(a_x))=arctan\ ((-4)/3.6)=312^"o"` [4th quadrant]

So the car's acceleration has magnitude 5.38 ms-2, and direction `312^@` from the positive x-axis.

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