Hello dear tutors, the following questions are derivative application and optimization. Solve on paper please because it makes it harder for me to understand when types up on computer. no need for explanation. I will give good feedback. Thank You

1. An object moves in a straight line according to the motion equation [8] s(t) = -2+3 + 9t2 + 5t, where's is the distance in meters, and t is in seconds. (a) Find the initial conditions (position, velocity, acceleration) and interpret their meaning. (b) Draw a sketch of the position time graph. (c) When is the particle at rest? (d) When does the object move in a positive direction?2. A closed box with a square base is to have a volume of 252 em'. The material to construct the box comes in different thicknesses, The bottom costs $0.05/em". the top costs $ 0.02/cm", and the sides cost $ 0.04/cm. Find the dimensions of the box that will minimize the cost a) Determine the dimension of the box that will minimize the cost of the production. b) What is the minimum cost?(d) When does the object move in a positive direction? (e) Draw a motion diagram for the object till t = 65 (f) What is the total distance travelled,during the first 6 seconds? (g) Is the object slowing down or speeding up at t = 4 s?3. Ship A is 40 km east of Ship B. If Ship A sails west at 30 km/h and Ship B, starting at the same time, sails north at 15 km/h find the time when the ships will be closest together