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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.
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