The Physics
Hypertextbook
Opus in profectus

# Graphs of Motion

## Summary

• On a displacement-time graph…
• slope equals velocity.
• the "y" intercept equals the initial displacement.
• when two curves coincide, the two objects have the same displacement at that time.
• straight lines imply constant velocity.
• curved lines imply acceleration.
• an object undergoing constant acceleration traces a portion of a parabola.
• average velocity is the slope of the straight line connecting the endpoints of a curve.
• instantaneous velocity is the slope of the line tangent to a curve at any point.
• positive slope implies motion in the positive direction.
• negative slope implies motion in the negative direction.
• zero slope implies a state of rest.
• The area under the curve is meaningless
• On a velocity-time graph…
• slope equals acceleration.
• the"y" intercept equals the initial velocity.
• when two curves coincide, the two objects have the same velocity at that time.
• straight lines imply uniform acceleration.
• curved lines imply non-uniform acceleration.
• an object undergoing constant acceleration traces a straight line.
• average acceleration is the slope of the straight line connecting the endpoints of a curve.
• instantaneous acceleration is the slope of the line tangent to a curve at any point.
• positive slope implies an increase in velocity in the positive direction.
• negative slope implies an increase in velocity in the negative direction.
• zero slope implies motion with constant velocity.
• the area under the curve equals the change in displacement.
• On an acceleration-time graph…
• slope is meaningless.
• the"y" intercept equals the initial acceleration.
• when two curves coincide, the two objects have the same acceleration at that time.
• an object undergoing constant acceleration traces a horizontal line.
• zero slope implies motion with constant acceleration.
• the area under the curve equals the change in velocity.
• The mathematical transformations between graphs of motion are shown below.  