Please answer all the questions in the attached file.

Requirements:

1. Please read the questions carefully.

2. Use grade 12 calculus level answers.

3. Answer in exact integers, fractions, multiples of ?, or radicals unless stated by the question to answer in decimal form (round to 2 decimal places).

4. Include step-by-step instructions and detailed answers in chronological order.

5. Maintain proper answer formatting.

1. The position of a particle moving along a straight line is given by the function S(t) = 2sint + cos2t, where S [cm] and t [seconds] Answer all questions for the interval te [0, 2x ] seconds, and account for all possible solutions! Use Interval Notation. Round your answers to the nearest hundredth (2 decimal places), if they are not exact integers, fractions, multiples of /7 or radicals. a) What is the velocity of the particle at t = 2.8 s ? b) What is the acceleration of the particle at t = 3.5 s ? c) When is the particle neither accelerating, nor decelerating? d) When does the particle change direction from positive to negative? e) When does the particle change direction from negative to positive? f) When is the particle moving away from the Origin? g) What is the maximum distance from the Origin? h) When is the velocity increasing? What are the minimum and maximum velocities of the particle? When is the particle speeding up? k) When is the particle slowing down? 1) What is the total distance travelled