NEED THE RIGHT ANSWERS WITH ALL THE PROPER STEPS FOR EVERY SINGLE QUESTION (PLEASE MAKE SURE YOUR HANDWRITING IS VERY CLEAR AND ORGANIZE). THANK YOU

QUESTION 1

The equation of motion for a particle moving along the y-axis is given as Ht} 2 212 8f + 3 for t t: 0. Part A: Find 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 % crnlmin l ch | rm i t (Note. The volume of a cone of height h and radius r is given by v = gym) Part A: Find the volume Vol sand in the container when I? : 4 cm, Indicate units of measure (10 points) Part B: Find the rate of Change of the votume of sand in the container, with respect to time, when n = 4 cm. Indicate units of measure. (20 points) Let f(x) be defined such that f(1) = 2 and f'(x) = cos(- + x), where 0