Analyzing Position versus Time Graphs: Conceptual Question| University Physics

Problem:

Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters.

Two graphs for positions of two cars, labeled car 1 and car 2, as functions of time are shown on the same set of axes. Time is measured on the positive x-axis and the position is measured on the y-axis. A grid is shown on the plane. The position of car 1 increases linearly from the point with coordinates (0,-3) to the point with approximate coordinates of (11.5, 4). Graph for car 1 crosses the x-axis at point with coordinates (5, 0) at time B. The position of car 2 smoothly increases from the point with approximate coordinates of (0, -0.5), crossing the x-axis at (1, 0) at time A, to the maximum at point with coordinates (6, 4) at time C, when the slope of the graph equals zero. Then the position smoothly decreases to a point with approximate coordinates of (12, -1), crossing the graph for car 1 at (9, 2.5) at time D, and crossing an x-axis again at (11, 0), at time E.

PART A. At which of the times do the two cars pass each other?

ANSWER: D

Two objects can pass each other only if they have the same position at the same time.

PART B. Are the two cars traveling in the same direction when they pass each other?

ANSWER: No

PART C. At which of the lettered times, if any, does car #1 momentarily stop?

ANSWER: None

The slope on a position versus time graph is the “rise” (change in position) over the “run” (change in time). In physics, the ratio of change in position over change in time is defined as the velocity. Thus, the slope on a position versus time graph is the velocity of the object being graphed.

PART D. At which of the lettered times, if any, does car #2 momentarily stop?

ANSWER: C

PART E. At which of the lettered times are the cars moving with nearly identical velocity?

ANSWER: A

Advertisements