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Home Concept Builders 1D Kinematics Dots and Graphs Help Help 11

Dots and Graphs - Questions 11 Help

The location and the slope of a line on a velocity-time graph is an indication of how an object is moving. A horizontal line (zero slope) indicates a constant velocity. The further such a line is above or below the axis, the faster that the object is moving. A line located above the axis of a v-t graph represents an object with a positive velocity and a line below the axis represents an object with a negative velocity. A sloped line is an indicator of a changing velocity. If the line slopes towards the axis, then the object is slowing down. And if the line slopes away from the axis, then the object is speeding up.

There are four similar versions of this question. Each includes two horizontal lines and four diagonal lines on a velocity-time graph. Here is one of the versions:
 

Version 1:

Consider the dot diagrams for Objects A, B, and C. The arrow represents the direction of motion. Match the motion of Objects A, B, and C to one of the lines on the graph. Numbers can be used only one time.

You have to match the motions of A, B, and C to one of the six lines on the position-time graph. That's going to require some good thinking and decision-making. The following should help:

Positive vs. Negative Velocity: For each object, you need to decide whether the velocity is positive or negative. Look at the arrow on the dot diagram; it indicates the direction that the object is moving. Typically a leftward motion is considered a negative velocity and a rightward motion is a positive velocity. On a v-t graph, a positive velocity is represented by a line that is located above the axis in the positive region (lines 1, 2, or 4) and a negative velocity by a line located below the axis in the negative region (lines 3, 5, or 6).

Constant Speed vs. Changing Speed: For each object, you will have to decide if the speed is constant or changing. On a dot diagram, equally-spaced dots are an indicator of a constant speed. When the distance between adjacent dots varies over time, the speed is changing. A constant speed motion will have to be matched to a horizontal line on a velocity-time graph (lines 2 or 6). On the other hand, a changing speed motion will have to be matched to a diagonal line on a velocity-time graph (lines 1, 3, 4, or 5)

Speeding Up vs. Slowing Down: The final decision you will have to make pertains to whether the object is speeding up or slowing down. On a dot diagram, if the dots get further and further apart, then the object is speeding up. When dots get closer and closer together, the object is slowing down. The speeding up motions correspond to lines on a velocity-time graph that are getting further from the time axis (lines 1 or 3). A slowing down motion corresponds to a line that is approaching the time axis (lines 4 or 5).

The following pages from The Physics Classroom Tutorial may provide additional background information and help with the topics in this Concept Builder:

Dot Diagrams

Velocity-Time Graphs: Meaning of Shape

Concept Builder Teacher Notes Directions