(Solved): The function \( s=t^{3}-3 t^{2}+3 t, 0 \leq t \leq 3 \), gives the position of a body moving on a c ...

The function \( s=t^{3}-3 t^{2}+3 t, 0 \leq t \leq 3 \), gives the position of a body moving on a coordinate line, with \( s \) in meters and \( t \) in seconds. a. Find the body's displacernent and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, If ever, during the interval does the body change direction? a. What is the body's displacement for the given time interval? m (Simplify your answer.) What is the average velocity for the given time interval? m/s (Simplify your answer.) b. What is the body's speed at \( t=0 \) ? \( \mathrm{m} / \mathrm{s} \) (Simplify your answer) What is the body's speed at \( t=3 \) ? \( \mathrm{m} / \mathrm{s} \) (Simplify your answer.) What is the body's acceleration at \( t=0 \) ? \( \mathrm{m} / \mathrm{s}^{2} \) (Simplify your answer.) What is the body's acceleration at \( t=37 \) \( m^{2} s^{2} \) (Simplify your answer.) c. When, if ever, during the interval does the body change direction? Select the correct choice below and, if necessary, fill in the answer box to cornplete your choice. A. \( 1= \) B. There is no solution.