question in image ## Problem StatementConsider an object moving along a line with the following velocity and initial position. Assume time \( t \) is measured in seconds and velocities have units of m/s. Complete parts (a) through (d) below.\[ v(t) = \sqrt{3} - 2\cos\left(\frac{\pi}{6}t\right), \]for \( 0 \leq t \leq 6; \, s(0) = 0 \)---### a. Determine the Direction of Movement#### Task:Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction.- **Positive Direction Interval:** - **Negative Direction Interval:** *(Type your answers in interval notation. Type exact answers, using \(\pi\) as needed.)*---### b. Find the Displacement#### Task:Find the displacement over the given interval.- **Displacement:***(Round to the nearest hundredth as needed.)*---### c. Find the Distance Traveled#### Task:Find the distance traveled over the given interval.- **Distance:***(Round to the nearest hundredth as needed.)*---### d. Determine the Position Function#### Task:Determine the position function \( s(t) \) using the Fundamental Theorem of Calculus. Check your answer by finding the position function using the antiderivative method.- **Position Function \( s(t) = \)**---

Name: question in image ## Problem StatementConsider an object moving along
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: question in image ## Problem StatementConsider an object moving along a line with the following velocity and initial position. Assume time \( t \) is measured in seconds and velocities have units of m/s. Complete parts (a) through (d) below.\[ v(t) =