Please help me with the following qs.

1.

A rock thrown vertically upward from the surface of the moon at a velocity of 32 m/sec reaches a height of s = 32t - 0.812 meters in t sec. a. Find the rock's velocity and acceleration at time t b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft?ds The accompanying figure shows the velocity v = dt = f(t) (m/sec) of a body moving along a coordinate line. a. When does the body reverse direction? b. When is it moving at a constant speed? c. Graph the body's speed for 0 = t = 10 d. Graph the acceleration, where defined Av (m/sec) 5- V = f (t ) (sec) t 10Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = - 2, u'(0) = - 5, v(0) = 1, and v'(0) =8. Find the values of the following derivatives at x = 0. d dx ( uv) b C d d. ( - 4v - 6u) dxFind the equation of the tangents to the curve y = cos x at x = 2' 2, and 2x. Graph the curve over the interval | - 2x, ? together with their tangents. Label each curve and tangent. What is the equation of the tangent (I) to the curve at x = - 2' y =The equation below gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds). Find the body's velocity, speed, acceleration, and jerk at time t =- 4 sec. $ = 1 - 7 cos t The velocity of the body at t= - sec is m/sec.Find the derivative of the following function. - 2 y = - (4x - 5)3 + 2 - 12 3x3 dy dx\fWhen a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the 200 rocket to keep it from breaking when it lands. The figure here shows the velocity data from the flight of the model rocket. Use the data to complete 1507 parts (a) through (9). 100- velocity (futsec) 50 -50 -100 2 6 8 10 12 Time after launch (sec)