Chapter 5: Constant Velocity

5.1 Introduction to Constant Velocity Motion

Constant velocity is a term used to describe a situation where an object moves at a constant speed in a straight line. In other words, the velocity of the object remains unchanged, which means that its speed and direction do not change over time. In future chapters we will discuss various types of motion—from constant acceleration to uniform circular motion. Consequently, it is important to keep track of which type of motion is being discussed when writing down equations and solving problems.

Learning physics is not the same as learning math. Oftentimes, in math classes, you will learn a fundamental theorem or equation that will always apply. You generally learn methods and techniques that apply to any problem, and it’s just a matter of sorting out the easiest way to solve a given problem. Physics is not like that. With physics, you need to keep track of the physical conditions that accompany each equation you receive.

For example, in this chapter, the condition that applies is obvious: the object must be moving with constant velocity. This imples that there is no change is speed or direction. Another way to say this is that the acceleration is zero. All of these statements say the same thing, so choose one that works for you and memorize it as the condition associated with the equations that follow.

5.2 The Importance of Constant Velocity Reference Frames

Constant velocity is a physically important concept because it allows us to simplify complex motion problems and make accurate predictions about the motion of objects. In many cases, objects in the real world do not move at a constant velocity for very long, but they may move at a constant velocity for short periods of time. By focusing on the constant velocity portions of an object’s motion, we can more easily understand the overall motion of the object.

In physics, constant velocity is often used as a reference frame for other types of motion. For example, when we observe an object moving at a constant velocity, we can describe its motion relative to this reference frame. This allows us to more easily compare the motion of different objects as well as understand the effects of forces and accelerations on the motion of these objects.

Constant velocity is also helpful in solving physics problems because it allows us to use simple kinematic equations to make predictions about an object’s motion. (Kinematics is the study of how things move. It focuses on describing the motion of an object, such as its position, velocity, and acceleration, without considering the forces that cause the motion). For example, if we know the velocity of an object at a certain time, we can use this information to calculate its position at a later time using a simple kinematic equation. This can be a very useful tool in solving problems related to the motion of objects.

5.3 Constant Velocity Equations:

Our first equation for constant velocity motion relates change in position to an object’s velocity as:

where:

• is the final position of the object
• is the initial position
• is the object’s velocity
• is the time (usually measured from to some future time).

This is a kinematic equation as it describes the motion of an object without a need to analyze the forces acting on it.

There’s another important, albeit redundant, statement:

which demonstrates that, in constant velocity problems, the final velocity is equal to the initial velocity. Thus, there is no need for any subscript at all and we can just write when referring to the velocity.

There is a final statement to be made which I have not yet given the basis for. We will discuss it in greater detail in Chapters 7 and 9. For now, write it down with the other constant velocity equations.

where:

• is the sum of all forces acting on an object
• is the mass of that object
• is the acceleration of the object
• is the zero vector.

This equation tells us that an object experiencing constant velocity motion has an acceleration of

Chapter Summary

This chapter introduced the concept of constant velocity motion, an important concept in physics that describes an object’s motion when its velocity—both speed and direction—remains unchanged over time. Constant velocity motion is central to kinematics, the study of how things move, and provides a useful reference frame for analyzing other types of motion. We also introduced some key equations to assist in the problem-solving process. Understanding constant velocity motion equips us to analyze and solve a range of physics problems.

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