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 .

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) with respect to time:

x(t) = ∫v(t)dt

x(t) = ∫(3.00 m/s + (4.00 m/s^2)t) dt

x(t) = (3.00 m/s)t + (2.00 m/s^2)t^2 + C

where C is the constant of integration. We can determine the value of C by using the given initial position:

x(1) = 1.00 m

(3.00 m/s)(1 s) + (2.00 m/s^2)(1 s)^2 + C = 1.00 m

C = -1.33 m

Substituting this value of C, we get:

x(t) = (3.00 m/s)t + (2.00 m/s^2)t^2 - 1.33 m

Simplifying:

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

Therefore, the best choice is E: 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