The velocity of an object is given by the expression v(t) = 3.00 m/s + ( 2.00 m/s³)t². Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.00 s. A)( 2.00 m/s)t + 1.00 m B)(3.00 m/s)t + ( 0.667 m/s3)t³ C)( 2.00 m/s)t D)0.667 m E)1.00 m + (3.00 m/s)t + ( 0.667 m/s³)t³

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The position of the object is given by the integral of the velocity with respect to time. Therefore, the position of the object is given by:$$x(t) = \int v(t) dt = \int (3.00 m/s + ( 2.00 m/s³)t²) dt = 3.00 m/s t + ( 0.667 m/s³)t³ + C$$where C is the constant of integration. To determine the value of C, we use the initial condition that the object is located at x = 1.00 m at time t = 0.00 s. Therefore, we have:$$x(0) = 1.00 m = 3.00 m/s (0) + ( 0.667 m/s³)(0)³ + C$$$$C = 1.00 m$$Therefore, the position of the object as a function of time is given by:$$x(t) = 3.00 m/s t + ( 0.667 m/s³)t³ + 1.00 m$$

The Velocity of an Object Is Given by the Expression