B. Directions: Show your solution to the following problems. The position vs. time graph below describes the motion of a runner. z (m) 3 t (s) t (s) 3 1. What is the magnitude of the velocity of the runner during the first 4 seconds? 2. What is the velocity of the athlete from t=4 s to 7 s?

Include a picture or description of your coordinate system (origin, positive direction).

2. The position of a drone as a function of time is given by *(t) = ( 8 i + 1.5 k) + (-3 î + 2 j) t – 0.5 t2 j The units are missing in the constant coefficients above, i.e., "0.5" should be "0.5 m/s2". Include the correct units on all the constant coefficients in your answers below. a. What is the x-position of the drone as a function of time? b. What is the y-position of the drone as a function of time? c. How far away is the drone from its starting position at t = 3s? d. What is the acceleration vector? е. What is the velocity vector as a function of time? (One way to do this is to take the time derivative of the position vector.) f. Make a sketch of the x, y, and z positions of the drone as function of time. You just need the general shape. time time time

V 0 A C. B 2. Two identical objects, A and B, move along straight, parallel, horizontal tracks. The graph above represents the velocity as a function of time for the two objects. a. At approximately which time or times, if any, are the objects moving at the same speed? If the objects are never moving with the same speed during the interval shown, indicate this explicitly. Briefly explain your answer. b. At approximately which time or times, if any, are the objects moving with the same acceleration? If the objects are never moving with the same acceleration during the interval shown, indicate this explicitly. Briefly explain your answer. At approximately which time intervals is object B moving at a greater speed than A? If the object B are never moving with the same speed during the interval shown, indicate this explicitly. Briefly explain your answer. d. If Object B has an initial position of Xb = -4.5m and Object A started at the origin, at approximately which time or times, if any,…