4. Suppose the position of an object moving horizontally after t seconds is given by the function s = f(t) = -6t3 + 36t² – 54t, where s is measured in feet, with s > 0 corresponding to positions right of the origin. When is the particle at rest? SHOW WORK!!! а. b. the interval [0,4], when is the particle moving to the right? SHOW WORK!!! c. What is the acceleration of the object when its velocity is 0? Include units. с.

A particle moves along the x-axis according to r(t) = 20t - 4t² m. Help on how to format answers: units. a. Determine the instantaneous velocity at each of the following times. At time t = 1s the instantaneous velocity is: At time t = 8s the instantaneous velocity is: b. Determine the instantaneous speed at each of these times. At time t = 1s the instantaneous speed is: At time t = 8s the instantaneous speed is: c. What is the average velocity between t = 1s and t = 8 s? Answer:

Suppose that critters are discovered on Mars that measure distance in boogles and time in bops. A. What would units of speed be in this system? Explain. B. What would units of velocity be in this system? Explain. C. What would units of acceleration be in this system? Explain.

A ball is thrown at an initial height of 90 feet at an initial velocity of 55 feet/second at an angle of 75 degrees. Given the parametric equations y = 16t2 + Vo · Sin(0)t + ho and r = Vo Cos(0)t. When doing calculations, carry 5 digits of accuracy, so your round off does not build up. a. What is the ball's height in 3 seconds? feet. b. When will the object hit the ground? seconds. c. How far horizontally will the ball be when it hits the ground? feet. d. When will the ball be at its maximum height? seconds. e. What is the ball's maximum height? feet. f. How far horizontally will the ball be when it reaches its maximum height? feet

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Hi, below is the explanation to the problem cited.  But I don't understand the answer to the last question #3: Determine its average acceleration during the 34.0 sec interval.  I am lost; can you help? Thanks! A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABCis 214 m, and the car completes the turn in 34.0 s. An x y coordinate system is shown. Three points A, B, and C are shown on the graph. These points are joined by a dotted curve. Point A is on the negative y-axis, point C is on the positive x-axis, while point B is in the fourth quadrant IV at an angle of −35° with the x-axis. From point A the curve initially moves rightward along a circular path, curves upward to cross B and then meets C. An arrow indicating the velocity at point A points horizontally and to the right. An arrow indicating the velocity at point C points vertically upward. 1. What is the acceleration when the car is at…