Motion in One Motion in One DimensionDimension

Velocity can be interpreted graphically

The velocity of an object can be determined if the object’s position is known at specific times along its path.

One way to determine this is to make a graph of the motion. pg41Physics Serway/Faugh (Holt)

A Graph Showing Constant Velocity

The Physics

Classroom

Pg 41

The object moves 4.0 m in the time interval between t = 0 s and t = 4.0 s.

The object moves an addi- tional 4.0 m in the time interval between t = 4.0 s and t = 8.0 s. From these data we see that the avg. velocity for these time intervals as 1m/s.

Because the average velocity does not change, the object is moving with a constant velocity of +1.0 m/s, and its motion is represented by a straight line on the position-time graph. Pg41 Physics Serway/Faugh (Holt)

Slope of the line = Avg. Velocity

For any position-time graph, we can also determine the average velocity by drawing a straight line between any two points on the graph and calculating the slope of that line. (Pg 41)

Slope =Rise over the Run

Just think of a step.

Position-Time graphs for 3 objects

Object 1 - has a constant positive velocity because position increases uniformly with time. (Its slope is positive)

Object 2 – has zero velocity because its position does not change. The object is at rest. (The slope of this line is zero.)

Object 3 – has a constant negative velocity because its position decreases with time. It moves to the west. (The slope of this line is negative.) Pg41 Physics Serway/Faugh (Holt)

A Graph Showing Changing Positive Velocity.

The Physics

Classroom

Comparison of Constant Velocity and Changing Positive Velocity

Instantaneous and Average Velocities may be different.

If the position-time graph is curved, velocity increases with time. It is moving through large displacement with each interval (pg42)

• Between t = 0 s and t = 2.0 s the object moves 8.0 m and its average velocity for this time interval is 4.0 m/s. (vavg = 8.0m/2.0s)

• Between t = 0 s and t = 4.0 s the object moves 32 m and its average velocity for this time interval is 8.0 m/s. (vavg = 32m/4.0s)

Different averagevelocitiesdependingupon the

time interval.

Pg41 Physics Serway/Faugh (Holt)

To Find Instantaneous velocity from the Position-Time graph

• Construct a straight line that is tangent to the position-versus-time graph at the point or instant in question.

• Calculate the slope of that line.