Graphing Motion Lecture

Graphing Motion V-t Graphs Finding velocity, acceleration, and distance from graphs

Graphing Motion Describe the motion of the object.

Position (m)

Position-Time Graph 6 4 2 0 0

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

The object starts at rest and moves away (+slope) from the origin at an increasing velocity.

Graphing Motion

Position (m)

Position-Time Graph 6 5 4 3 2 1 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1

Time (sec)

What is the velocity of the object at 0.4 sec? Draw a line tangent to the slope at that point and find the slope of the line. V = 3.4 m/s

Graphing Motion What does the velocity-time graph of this motion look like?

Velocity (m/s)

V e lo city-T im e G ra ph

12 9 6 3 0 0

0.2

0.4

0.6 T im e (s e c)

0.8

1

1.2

Graphing Motion What is the total displacement of the object?

Velocity (m/s)

V e lo city-T im e G ra ph

12 9 6 3 0 0

0.2

0.4

0.6

0.8

1

T im e (s e c)

Find the area under the curve. Area = ½ v•t

1.2

Graphing Motion What is the acceleration of the object?

Velocity (m/s)

Velocity-Time Graph

12 9 6 3 0 0

0.2

0.4

0.6 Tim e (se c)

Find the slope of the line.

0.8

1

1.2

Graphing Motion What does the acceleration-time graph of this motion look like?

Acceleration (cm/s/s)

Acceleration-Time 15 10 5 0 0

0.2

0.4

0.6

Time (s)

0.8

1

Graphing Motion • Position-time Graphs (d-t) velocity – Slope (∆ y/∆ x) = ∆ d/∆ t = ___________

• Velocity-time Graphs (v-t) – Slope (∆ y/∆ x) = ∆ v/ = ____________ acceleration ∆ tv • t = ________________ – Area (b • h or ½ b •h) = displacement

• Acceleration-time Graphs (a-t) – Area (b • h or ½ b •h) = a • t = ________________ change in velocity