Explain the following questions and answers:

Which of the following statements must be true for a falling object that has been dropped from rest near the surface of Earth? The derivative of the distance the A. object falls with respect to time equals 9.8 m/s2. B. The object falls a vertical distance of 9.8 m during the first second only. C. The object falls a vertical distance of 9.8 m during each second. D. The speed of the object as it falls is a constant 9.8 m/s. V E. The speed of the object increases by 9.8 m/s during each second.Question Proof/Work/Explanation 1. The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation: v( t ) =4 + 2+3 What is the acceleration of the automobile at t = 2 s? A. 2 m/s2 B. 16 m/s2 C. 20 m/s2 V D. 24 m/s E. 28 m/s 2. How far has the automobile traveled in the interval between t = 0 and t = 2 s? V A. 16 m B. 20 m C. 24 m D. 32 m E. 72 m3. A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball's velocity v is given as a function of time t by the equation v(t) = 5 - 10t. The positive direction is upward. What is the ball's acceleration at time t = 1 s? V A. -10 m/s B. -5m/s2 C. 0 D. 5 m/s2 E. 10 m/s2 4. If the ball reaches the ground at t = 2.0 s, what is the height of the building? A. 5m V B. 10 m C. 15 m D. 20 m E. 30m 5. At what time does the ball reach its maximum height above the building? A. 0.2 s B. 0.4 s V C. 0.5 s D. 1.0 s E. 2.0 s6. The velocity of a particle moving along the x- axis is given as a function of time by the expression v(t) = 3.0t- - 2.0t + 4.0, where v is in meters per second and t is in seconds. What is the acceleration of the particle at t = 2.0 s? 4.0 m/s B. 6.0 m/s2 C. 8.0 m/s V D. 10.0 m/s E. 12.0 m/s