Graphical Representation of Motion in One Dimension (Part Two)
Velocity–Time Graph
First: Summary:
► 𝑥-axis → Time (𝑡)
𝑦-axis → velocity (𝑣)
► If the graph is horizontal → the velocity is constant (𝑎 = 0).
If the graph is not horizontal → the velocity is changing (𝑎 ≠ 0).
► If the graph is in the first quadrant → the velocity is eastward.
If the graph is in the fourth quadrant → the velocity is westward.
► If the graph slopes upward in the first quadrant → the object's velocity increases in magnitude
(eastward).
If the graph slopes downward in the fourth quadrant → the object's velocity increases in magnitude
(westward).
► If the graph is a straight line → the acceleration is constant.
If the graph is a curved line → the acceleration is changing.
► If the graph is a straight line → the magnitude of the acceleration equals the slope of the graph.
If the graph is a curved line:
● The instantaneous acceleration equals the slope of the tangent at that instant.
● The average acceleration equals the slope of the straight line connecting the initial point and
the final point.
Main idea: The slope of a velocity–time graph represents acceleration (𝑎).
The area under the velocity–time graph represents displacement (𝛥𝑥).
(m/s)
Δy
slope =
Δx
=a
Area=Δx
t (s)
Velocity–Time Graph
First: Summary:
► 𝑥-axis → Time (𝑡)
𝑦-axis → velocity (𝑣)
► If the graph is horizontal → the velocity is constant (𝑎 = 0).
If the graph is not horizontal → the velocity is changing (𝑎 ≠ 0).
► If the graph is in the first quadrant → the velocity is eastward.
If the graph is in the fourth quadrant → the velocity is westward.
► If the graph slopes upward in the first quadrant → the object's velocity increases in magnitude
(eastward).
If the graph slopes downward in the fourth quadrant → the object's velocity increases in magnitude
(westward).
► If the graph is a straight line → the acceleration is constant.
If the graph is a curved line → the acceleration is changing.
► If the graph is a straight line → the magnitude of the acceleration equals the slope of the graph.
If the graph is a curved line:
● The instantaneous acceleration equals the slope of the tangent at that instant.
● The average acceleration equals the slope of the straight line connecting the initial point and
the final point.
Main idea: The slope of a velocity–time graph represents acceleration (𝑎).
The area under the velocity–time graph represents displacement (𝛥𝑥).
(m/s)
Δy
slope =
Δx
=a
Area=Δx
t (s)
