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Home Concept Builders 1D Kinematics Dots and Graphs Help Help 4

Dots and Graphs - Questions 4 Help

The slope of a position-time graph provides insight about the velocity of the object. By carefully interpreting the slope of the line and how it changes over time, one can determine the manner in which the object is moving - constant speed, speeding up, slowing down, and the direction of motion.

There are four similar versions of this question. Each version includes fourcurved lines and two diagonal lines on a position-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. A positive velocity is represented by a line with positive slope (lines 1, 2, or 4) and a negative velocity by a line with negative slope (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 straight line on a position-time graph (lines 2 or 6). On the other hand, a changing speed motion will have to be matched to a curved line on a position-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 line on a position-time graph that are becoming steeper with time (lines 4 or 5). A slowing down motion corresponds to a line that is becoming flatter over the course of time (lines 1 and 3).

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

Position-Time Graphs: Meaning of Shape

Dot Diagrams

Concept Builder Teacher Notes Directions