Arizona State University| PHY 121: Univ Physics I: Mechanics|Homework 1-2| Velocity from Graphs of Position versus Time

Problem:

An object moves along the x-axis during four separate trials. Graphs of position versus time for each trial (with the same scales on each axis) are shown in the figure.

The figure shows four graph, labeled trial A, trial B, trial C and trial Deach of which shows the position as a function of time. Time is measured on the positive x-axis and the position is measured on the y-axis. On graph trial A the position increases linearly from the origin. On graph trial B the position smoothly increases from the point, which lies on the negative y-axis, forming a convex curve and intersecting the positive x-axis. On graph trial C the position remains constant at some positive value. On graph trial D the position decreases linearly from the point, which lies on the positive y-axis intersecting the positive x-axis.

PART A. During which trial or trials is the object’s velocity not constant?

ANSWER: Trial B

The graph of the motion during Trial B has a changing slope and therefore is not constant. The other trials all have graphs with constant slope and thus correspond to motion with constant velocity.

PART B. During which trial or trials is the magnitude of the average velocity the largest?

ANSWER: Trials B and D

While Trial B and Trial D do not have the same average velocity, the only difference is the direction! The magnitudes are the same. Neither one is “larger” than the other, and it is only because of how we chose our axes that Trial B has a positive average velocity while Trial D has a negative average velocity. In Trial C the object does not move, so it has an average velocity of zero. During Trial A the object has a positive average velocity but its magnitude is less than that in Trial B and Trial D.

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