An object's velocity is measured to be *v*_{x}(*t*) = *α *− *βt*^{2}, where *α* = 4.00 m/s and *β* = 2.00 m/s^{3}. At *t* = 0 the object is at *x* = 0.

(a) Express the object's position as a function of time.

(b) Express the object's acceleration as a function of time.

(c) What is the object's maximum *positive* displacement from the origin?

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