Calculus please help Thank you.I need 7-9.Show ur work

") . The position of a particle is given by the equation s = f(t) = t - 27t + 240t (6 pts.) Where t is measured in seconds and s in centimeters. (a) Find the velocity at time t. What is the velocity after Is? (b) When is the particle at rest? (c) When is the particle moving in the positive direction, when is the particle moving in the negative direction? (d) Draw a diagram to represent the motion of the particle. (c) Find the total distance traveled by the particle during the first 15 seconds. (f) Find the acceleration at time t and after 10 seconds. 8) The volume of a rectangular box with a square base remains constant at 1, 100 em as the area of the base increases at a rate of 2 cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 12 cm long (Leave your answer in fraction form). (5 pts.) Hint: V = length. width.height = Area.height 9) Graph of the velocity function is shown below, where t is measured in seconds. When is the particle speeding up? When is it showing down? (4 pts.) 2 0 4 6