For the following scenario, take your coordinate axis to have increasing values of x to the right. The position of a particle moving along the x axis is given by x (t) = 3.0m + (5.0m/s)t for 3 seconds. After the 3 seconds, the particle turns around and his position is observed to follow the new motion given by x (t) = 18.0m - (7m/s)t for 2 seconds. What is the particle's initial position for the first motion? b) What is the particle's velocity for the first 3 seconds? C) What is the particle's final position after the first 3 seconds? d What is the final position after the end of the journey (after traveling the 5 seconds)? e What is the particle's total displacement after traveling the 5 seconds? f) What is the particle's total distance after traveling the 5 seconds? g Draw the corresponding position vs time graph for the 5 seconds of motion. h) Draw the corresponding velocity vs time graph for the 5 seconds of motion.Problem 1) A runner in a relay race runs 20 m north, turns around and runs south for 30 m, then turns north again and runs 40 m. The entire run took 30 seconds. (Choose a coordinate system with increasing values of position north). a) What was the distance traveled? b) What was the runner's displacement? c) What was the average speed ofjthe runner? d) What was the average velocity of the runner? Problem 2) The position of a moving object is given by the following function x0) = 2.0m + (6.0m/s)r a) What is the initial position of the object? is) What is the velocity of the object? o) What displacement does the object move from t = 1.35 tot = 2.45? d} Draw a position vs time graph for the moving object from t = US to I = 3.6.9 e) Draw a velocity vs time graph for the moving object from I 2 OS to t = 3.63 1') Verify that you can interpret the area underneath the velocity vs time graph as the displacement traveled by the object. Another way of saying it... use the velocity vs time graph to find the displacement of the moving object from i.\" = 1.35 to I = 2.45