NEED THE RIGHT ANSWERS WITH ALL THE PROPER STEPS FOR EVERY SINGLE QUESTION (PLEASE MAKE SURE YOUR HANDWRITING IS VERY CLEAR AND ORGANIZE AND IF YOU CAN TYPE IT THAT WOULD BE EVEN BETTER. THANK YOU

QUESTION 1

The equation of motion for a particle moving along the yams is given as Ht} 2 2:2 8f + 3 for is 0. Part A: :ind the velocity and acceleration functions. (10 points] Part B: Describe where the particle changes direction and the intervals where the particle speeds up or slows down. (20 points} Sand is being poured into an open right circular cone container, as shown in the gure, The height of the container is 8 cm, and the diameter of the opening is 8 cm Sand is being poured in so that its depth h is changing at a constant rate of % crnimin 8cm l T i (Note The volume of a cone of height h and radius r is given by v : %ur2h) Part A: Find the volume Vol sand In the container when n : 4 cm, Indicate units of measure (10 points) Part E: Find the rate of Change of the volume of sand in the container, with respect to time, when h : 4 cm. Indicate units of measure. (20 points) Let f(x) be defined such that f(1) = 2 and f'(x) = cos(-7+ x), where 0