Let the position at time t seconds of a particle moving in a coordinate line be given by s(t) = cos(3t) centimeters.(a) Find its velocity v(t) = s0(t) at time t.(b) Show that 9s(t)2 +v(t)2 = 9.(c) Find its acceleration a(t) = v0(t) = s00(t) at time t.

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-5-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) = The terminal velocity is Submit m/s. m/s

A calculus student bungee jumps off a bridge. Her height is modeled in meters as h(t) = 15(1+e-t/3cos(t)) a) Plot the height of the jumper as a function of time from t=0 to t=20.   b) What is the derivative of h(t)? You will need the fact that d/dx (e-t/3) = -1/3e-t/3   c) Use the previous part to determine when jumper first bounces back  up-ward (round to the nearest hundredth of a second). Your solution process will involve an inverse tangent.   d) What is the maximum velocity of the jumper within the first 20 seconds?