The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s3)t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s. A) (4.00 m/s)t + 1.00 m B) (3.00 m/s)t + (1.33 m/s3)t³ C) (4.00 m/s)t D) 1.33 m E) 1.00 m + (3.00 m/s)t + (1.33 m/s³)t³

Question

Quizplus · Accepted Answer

To find the position of the object as a function of time, we need to integrate the velocity function.

∫v(t) dt = ∫(3.00 m/s + (4.00 m/s^3)t) dt = 3.00t + (1.00 m/s^2)t^2 + C

Since we know the object is located at x = 1.00 m at time t = 0.000 s, we can solve for C:

1.00 m = 3.00(0.000 s) + (1.00 m/s^2)(0.000 s)^2 + C

C = 1.00 m

So the position function is:

x(t) = 3.00t + (1.00 m/s^2)t^2 + 1.00 m

Simplifying this expression gives:

x(t) = 1.00 m + (3.00 m/s)t + (1.33 m/s^3)t^3

Therefore, the correct choice is E.

The Velocity of an Object Is Given by the Expression