Introduction to Uniform Motion

Relevance of the Topic:

Kinematics is the branch of Physics that studies the motion of bodies, without worrying about the causes that provoke it (addressed in Dynamics). Uniform Motion (UM) is one of the basic concepts of Kinematics, being fundamental for the understanding of other topics within Physics, such as Uniformly Varied Motion (UVM), kinetic energy, among others. The ability to understand and apply concepts of uniform motion is therefore essential for the development of a solid knowledge in Physics.

Contextualization:

Uniform Motion occurs when a body moves with constant speed in a straight trajectory. This implies that the body covers equal distances in equal time intervals.

This concept is the basis for the study of other types of motion in Physics, serving as an essential building block for the understanding of the discipline. Without a good understanding of how Uniform Motion works, more complex concepts in physics can become confusing and intimidating.

Furthermore, understanding Uniform Motion is applicable to many real-life situations, including trips, sports, and even the analysis of stock charts. Therefore, the concepts learned in this section have direct applications and can be useful in many aspects of everyday and professional life.

In this section, you will learn about the characteristics of Uniform Motion, learn to calculate the average speed, and apply these concepts to determine the position or time for displacements.

Theoretical Development: Uniform Motion

Concepts and Definitions:

• Uniform Motion: is the movement of a body that occurs when its speed is constant over time, that is, its magnitude, direction, and sense do not vary. The motion is rectilinear, that is, it occurs in a single direction and sense.

• Speed: is the magnitude that expresses how quickly a body moves. In UM, the speed is constant and equal to the average speed. It is expressed as the ratio between displacement and time interval.

• Space: in Physics, it is the distance or displacement of a body in relation to a reference point. In UM, the measure of space corresponds to the product of speed by time.

• Time: is the physical magnitude that allows measuring the duration or separation of events. In UM, time is a magnitude that makes it possible to calculate the distance traveled by a body through speed.

Fundamental Formula of Uniform Motion:

• In UM, the formula that associates the three basic concepts (speed, space, time) is: s = v.t, where:
  • s is the space or distance traveled by the body,
  • v is the constant speed at which the body moves,
  • t is the considered time interval.

Practical Examples:

• Example 1: A car travels on a straight road at a constant speed of 80 km/h. How much space has it covered after 2 hours? Just apply the fundamental formula of UM: s = v.t, where v = 80 km/h and t = 2 h. Thus, the car covered s = 80 * 2 = 160 km.

• Example 2: A train travels at a constant speed of 60 km/h. How long does it take to travel a distance of 120 km? Using the formula t = s/v, where s = 120 km and v = 60 km/h, the time is t = 120/60 = 2 h. Therefore, the train takes 2 hours to travel 120 km.

UM Graphs:

• The most common graph to describe UM is the space-time graph (s x t). In it, UM is represented by a line inclined in relation to the time axis, which reflects the constant speed of the motion. The slope of the line is numerically equal to the speed of the motion.

Memorable note: Constant speed is not synonymous with inertia! Even when moving at a constant speed, a body can be accelerated if the direction or sense of motion changes. This is the underlying principle of uniform circular motion, to be explored in future sections.

Detailed Summary

Key Points:

• Uniform Motion is a type of motion in which the body's speed remains constant over time. That is, there is no acceleration or deceleration; the body moves at a constant speed in a specific direction.
• In the discussion of Uniform Motion, three elements are crucial: Speed (v), Space (s), and Time (t).
• Speed (v) in uniform motion is constant and is defined as the ratio between displacement and time: v = s/t.
• Space (s) is the distance traveled by the body. In Uniform Motion, space is calculated by the product of speed by time: s = v.t.
• Time (t), in this context, is the interval during which the motion occurs.
• The equation s = v.t is fundamental in the analysis of Uniform Motion. It provides a direct way to calculate any of these three variables if the other two are known.
• In Uniform Motion, the space versus time graph (s x t) is a straight line whose slope is equal to the speed.

Conclusions:

• Uniform Motion is a fundamental concept that helps understand other topics within physics, such as Uniformly Varied Motion (UVM) and Kinetic Energy.
• The speed in Uniform Motion is constant and is given by the ratio between displacement and time.
• We can use the formula s = v.t to calculate the distance traveled or the time needed to travel a certain distance.
• In the space and time graph of Uniform Motion, speed is represented by the slope of the line.

Exercises:

1. A cyclist travels at a constant speed of 15 km/h. How long will it take for him to travel a distance of 60 km?
2. A train travels at a constant speed of 50 km/h. How much space will it have covered after 3 hours?
3. A plane flies at a constant speed of 900 km/h. If it flies for 2 hours, what will be the distance traveled?