Introduction

Relevance of the Topic

Graphs of Uniform Motion (MU) are essential for understanding Kinematics, the first major division of Physics. MU is a fundamental concept, representing motion with constant velocity and no acceleration. This type of motion is often observed in our daily lives, from the trajectory of a car on a highway to the uniform rotation of the Earth.

Contextualization

Graphs of Uniform Motion are an integral part of the Kinematics unit. After understanding important kinematic quantities such as position, displacement, velocity, and acceleration, this topic provides a powerful visual way to understand and represent these quantities over time. Not only does it allow for a more intuitive analysis of uniform motion, but it also serves as a basis for learning other types of motion, such as Uniformly Varied Motion (MUV) and motion in two and three dimensions.

Theoretical Development

Components

• Uniform Motion (MU): It is a type of motion in which the object travels equal distances in equal times, regardless of the direction of motion. The velocity, in this case, is constant, and the graph of position versus time (x vs t) is a straight line.

• Position vs Time Graph (x vs t): In this graph, the object's position is represented on the vertical axis (y) and time on the horizontal axis (x). For MU, the slope of the line is the velocity of the motion.

• Velocity vs Time Graph (v vs t): Here, the object's velocity is represented on the vertical axis and, again, time on the horizontal axis. For MU, the line is horizontal, indicating that the velocity is constant and does not vary with time.

• Displacement vs Time Graph (d vs t): The object's displacement (distance traveled relative to the initial position) is represented on the vertical axis and time on the horizontal axis. For MU, the graph is an ascending line whose slope is equal to the velocity of the motion.

Key Terms

• Position (x): It is the location of an object in space relative to a reference point. In the context of MU, it is the object's position at a given moment in time.

• Displacement (d): It is the difference between the final position and the initial position of an object.

• Velocity (v): It is the rate of change of displacement over time. In the case of MU, the velocity is constant and independent of time.

• Time (t): It is the continuous and indefinite period in which events occur and are sequenced. In MU, time is linear and can be measured in fixed units.

Examples and Cases

• Example 1: Identifying Uniform Motion in Graphs:

  • Case (a) - Position vs Time Graph (x vs t): In this graph, if the line is an ascending or descending straight line, the motion is not uniform. However, if it is a horizontal line, regardless of the slope, the motion is uniform with constant velocity.

  • Case (b) - Velocity vs Time Graph (v vs t): This graph will always be a straight horizontal line in uniform motion. The slope is zero, indicating that the velocity does not vary and is constant.

  • Case (c) - Displacement vs Time Graph (d vs t): In this case, if the line is a straight line with a constant slope, the motion is uniform. If the slope is zero, the velocity is zero, indicating that the object is at rest.

• Example 2: Calculating Velocity in Uniform Motion from the Graph:

  • Given a linear Position vs Time Graph (x vs t) with a magnitude 2 slope, the velocity of the object is 2 units of position per unit of time (2 m/s, for example). This is one of the main uses of MU graphs - determining the velocity of the motion. Here, velocity is determined by the slope of the line.

• Example 3: Finding Displacement in a Given Time Interval in Uniform Motion using the Displacement vs Time Graph (d vs t):

  • Given a linear Displacement vs Time Graph (d vs t) where the slope is 3, the object's displacement after 4 seconds is 12 units of displacement (for example, 12 meters). In this case, the area under the line represents the displacement. And, as the area of a rectangle is the base multiplied by the height, the displacement is obtained by multiplying the time interval by the slope value. Here, 3 (the slope) times 4 (the time interval) equals 12 (the displacement).

It is important to emphasize that all these concepts and examples can be applied from any of the three graphs (x vs t, v vs t, and d vs t), as they are interconnected and offer different perspectives of the same uniform motion.

Detailed Summary

Key Points

• Uniform Motion (MU): It is a type of motion in which the velocity is constant over time, so that the object travels equal distances in equal time intervals. To represent this type of motion, we use straight lines on the graphs.

• MU Graphs: They are visual representations of physical quantities (position, displacement, and velocity) as a function of time. In MU, the position, velocity, and displacement graphs are, respectively, a straight line, a horizontal constant, and a line with a constant slope.

• Interpretation of Graphs: Correctly reading the graphs allows us to understand the motion. The slope of the lines on the graphs provides the velocity of the motion, allowing us to calculate displacements in specific time intervals.

Conclusions

• Constant Velocity: In MU, the velocity is a constant. This means that at any point in the motion, the velocity will always be the same.

• Relationship between Graphs: The position, velocity, and displacement graphs as a function of time are interconnected and provide the same information about the motion, but in visually different ways.

• Reading and Data Extraction from Graphs: Correctly reading the graphs allows us to extract various information about the motion, including velocity, displacement, and travel time.

Exercises

1. Given a Velocity vs Time Graph (v vs t) with a horizontal line at the 15 m/s mark, what is the velocity of the motion? And what type of motion is represented?
2. In the Displacement vs Time Graph (d vs t), how can we find the displacement in any time interval? Use the line represented with a slope of 4 as an example.
3. What is the difference between the Position vs Time Graph (x vs t) of a MU and a MUV? Describe the characteristics of each and how to identify them from the graph.