A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 . How many times does the particle change direction as t increases from to −3 to 3?

In 8 seconds, a bug travels along the line y=2. The position of the bug along y=2 is x(t)=1/3t^3 - 7/2 t^2 + 10t -2. At what times does the spider turn around? Over what intervals does the spider slow down?

The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial velocity of the object is v(0) 11 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. meters

What is the maximum height of the ball and when does it hit the ground if a ball is thrown with a velocity of 40ft/s, its height (in feet) after t seconds is given by h(t)=-16t2+40t.