Writing Assignment 3 1. Consider an object moving along a line with the given acceleration a(t)=6t + 12, initial velocity 12(0) 2 9 m/S and initial position 5(0) 2 0. Assume time t is measured in seconds and acceleration have units of 111/52. a. Find the velocity v(t) and position 50:) ofthe object. 120:) = 50:) = b. Graph the velocity v(t) and determine when the motion is in the positive direction and when it is in the negative direction. Positive direction: Negative direction: c. Find the displacement over the interval [0, 5]. Displacement: I d. Find the distance traveled over the interval [0, 5] Distance: 2. Assume function g , for all real numbers, has a positive derivative, and g (3) = 0. Which of the following statements must be true of the function: F(x) = g(t)at Hint: You need to apply Fundamental Theorem of Calculus (part 1). Give reason for your answers. a. F is a differentiable function of x. b. F is a continuous function of x. c. The graph of F has a horizontal tangent at x = 3. d. F has a local maximum at x = 3. e. F has a local minimum at x = 3. f. The graph of F has an inflection point at x = 3. 3