The velocity of an object is given by the expression ,where t is in seconds.Determine the position of the object as a function of time if it is located at at time . 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 as a function of time, we can integrate the velocity function:

∫(11t - 4t^2) dt = (11/2)t^2 - (4/3)t^3 + C

where C is the constant of integration.

Using the given initial condition that the object is located at 1.00 m at time 0, we can solve for C:

(11/2)(0)^2 - (4/3)(0)^3 + C = 1.00

C = 1.00

Thus, the position function is:

x(t) = (11/2)t^2 - (4/3)t^3 + 1.00

Substituting t = 1.33 s (the given time), we get:

x(1.33) = (11/2)(1.33)^2 - (4/3)(1.33)^3 + 1.00 ≈ 2.67 m

Therefore, choice E is the correct answer, which gives the position function as:

x(t) = 1.00 m + (3.00 m/s)t + (1.33 m/s^2)t^2

The Velocity of an Object Is Given by the Expression