Position-Time Graphs & Velocity Video Lessons

Concept

Problem: The figure below shows the position-versus-time graph for a moving object. At which lettered point(s):(a) Is the object moving the slowest?(b) Is the object moving the fastest?(c) Is the object at rest?(d) Is the object moving to the left?

FREE Expert Solution

This problem asks us to describe the direction and relative magnitude of the object's velocity at various points based on its position-time graph.

Anytime we're given a position, velocity, or acceleration graph to work with, a PVA diagram like the one below can help remind you of the relationships between the three functions.

$\mathbit{P}\begin{array}{c}{\mathbf{←}}\\ {\mathbf{\to }}\end{array}\underset{{\mathbit{s}}{\mathbit{l}}{\mathbit{o}}{\mathbit{p}}{\mathbit{e}}}{\overset{{\mathbit{a}}{\mathbit{r}}{\mathbit{e}}{\mathbit{a}}}{\mathbit{V}}}\begin{array}{c}{\mathbf{←}}\\ {\mathbf{\to }}\end{array}\mathbit{A}$

Moving left to right, we take the slope of the graph—the slope of a position graph is the velocity

Horizontal lines have zero displacements (Δx) and zero slopes. The diagram below demonstrates how magnitude of a slope varies.

(a) We're asked to determine at which point the object is moving the slowest.

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Problem Details

The figure below shows the position-versus-time graph for a moving object. At which lettered point(s):
(a) Is the object moving the slowest?
(b) Is the object moving the fastest?
(c) Is the object at rest?
(d) Is the object moving to the left?