Question: The position vs. time graph below represents the motion of an object. Use the graph to answer the following questions.

(a) Determine the average velocity of the object between t = 0 and t = 5 seconds.

(b) At what time does the object have zero instantaneous velocity?

(c) Calculate the object's displacement between t = 0 and t = 5 seconds.

(d) Is the object moving at a constant speed between t = 5 and t = 10 seconds? Justify your answer.

Answer:

(a) The average velocity is calculated by dividing the change in position (displacement) by the change in time. Average velocity = (final position - initial position) / (final time - initial time) In this case, the final position at t = 5 seconds is 20 meters, and the initial position at t = 0 seconds is 0 meters. The final time is 5 seconds, and the initial time is 0 seconds. Average velocity = (20 - 0) / (5 - 0) = 4 meters per second.

(b) The object has zero instantaneous velocity when its tangent line to the position vs. time graph is horizontal (slope = 0). From the graph, we can see that the object has zero instantaneous velocity at t = 2 seconds and t = 8 seconds.

(c) Displacement is the change in position of an object, calculated by subtracting the initial position from the final position. In this case, the final position at t = 5 seconds is 20 meters, and the initial position at t = 0 seconds is 0 meters. Displacement = final position - initial position = 20 - 0 = 20 meters.

(d) To determine if the object is moving at a constant speed between t = 5 seconds and t = 10 seconds, we need to examine the slope of the position vs. time graph during that interval. If the slope remains constant (a straight line), the object is moving at a constant speed. From the graph, we can see that the slope between t = 5 seconds and t = 10 seconds is different at various points, indicating that the speed of the object is changing. Therefore, the object is not moving at a constant speed between t = 5 and t = 10 seconds.

Note: The graphical analysis of motion provides valuable information about the object's velocity, displacement, and changes in speed, all of which help in understanding the object's motion.