What Are The X- And Y-components Of The Velocity Vector Shown In The Figure? (figure 1)

The velocity of an object is how fast it is moving. Velocity is defined as the displacement of an object over a given time period.

In physics, velocity is described as linear motion in a constant direction. There are three vectors that define the velocity of an object: the x-component, y-component, and z-component.

All three components must be known to find the full velocity of an object. Depending on which two components are known, different equations must be used to find the missing component.

This article will explain what the x-, y-, and z-components are, how to determine which two components are known, and how to calculate the full velocity vector of an object using these components.

Components of velocity

Velocity is a measurement of how far something moves in a given period of time. Velocity is expressed as the speed (how fast something moves) and direction it moves.

Velocity is always stated as a vector, which means it has a magnitude (how fast it moves) and direction. The magnitude of velocity is always determined by the sum of two components: the x-component and the y-component.

The x-component (also called lateral velocity) is the difference in speed between the right and left side of an object moving forward. The y-component (also called longitude velocity) is the difference in speed between the top and bottom of an object moving forward.

In figure 1, these two components are what make up both vectors shown. The white arrow represents the x-component, or lateral velocity, while the green arrow represents the y-component, or longitude velocity.

Relationship between x-, y-components, and vx, vy

The x- and y-components of the velocity vector shown in the figure are vx = 4 m/s and vy = 2 m/s. The magnitude of the velocity is their sum, which is 6 m/s.

The x-component of the velocity is vx, which is 4 m/s in this case. The y-component of the velocity is vy, which is 2 m/s in this case.

Remember: Velocity consists of two components,speed and direction. We can always break down the total velocity into a magnitude (speed) component and a direction component.

We can also break down the total velocity into an x-component and a y-component. The x-component of the velocity is called vx, and it represents the speed component in the direction that you are facing (or moving). The y-component of the velocity is called vy, and it represents the speed component in the direction that you are facing (or moving).

Examples of x- and y-components

The x- and y-components can be illustrated with a few examples. Consider a car moving in a straight line at some constant speed.

The car’s velocity is its speed (how fast it moves) plus the direction it moves in. The car has a constant speed, so its velocity is purely in the forward direction.

Now consider a bicycle moving in a circular path around a post. The bicycle has some constant speed, so its velocity is purely in the forward direction. Again, consider a bullet moving toward a target. Its velocity is purely in the forward direction due to its high speed and precision.

Now let’s consider an object that moves at some angle to the x- and y-axes (see Figure 1). In this case, its velocity must have both an x- and y-component—it moves not only in the forward direction but also to the right. A typical example of this is a ball rolling diagonally across a floor.

Combining components to find final velocity

Now that you can find the x- and y-components of the velocity vector, you can combine them to find the final velocity. The final velocity is the speed at which an object will move in a particular direction.

The math to do this is not difficult, and you can go back to your notes on vectors if you need a refresher. Here’s how it works:

First, add the x-components together, then add the y-components together. Then, divide the first number by two, and multiply that number by the second number. The result is your final velocity!

For example, say we have two objects moving at velocities of 10 meters per second (m/s) in the x-direction and 5 m/s in the y-direction. To find their total velocity, we would simply add up their x-components and their y-components: (10 m/s + 5 m/s) = 15 m/s.

Understanding the diagram

A velocity vector diagram is a graphical way to understand the components of velocity. It uses an orthogonal (perpendicular) plane to represent the velocity of an object relative to some other object or reference point.

In this case, the reference point is Earth’s surface, or geoid, which is a model of Earth’s shape. The direction away from the geoid is called z-axis and represents vertical displacement.

The x-axis represents horizontal displacement (to your left or right) and the y-axis represents depth displacement (below you).

By knowing the length and direction of each vector, you can determine all of the components of velocity. In this case, the satellite is moving at a constant speed in a constant direction, so all three vectors are the same length and direction.

Diagram showing vector components

The x- and y-components of the velocity vector shown in Figure 1 are the components of the overall velocity vector in the x- and y-directions, respectively.

Velocity can be defined as a rate of change of position. In this case, the position is relative to a given frame of reference, typically earth based.

The more specific definition of velocity is the rate at which an object changes its position with respect to time.

Therefore, velocity can be expressed as an angular displacement per unit time or as a linear displacement per unit time. Both are valid definitions of velocity!

The x- and y-components can be found by dividing the overall velocity (v) by two: vx = v / 2 and vy = v / 2.

Example using vector components with velocities

Now that you understand the basics of velocity vectors and their components, let’s look at a practical example.

Suppose you are walking along a straight street at a constant speed of 2 meters per second, in the direction indicated by the red arrow in the figure below. What are the x- and y-components of your velocity vector?

To answer this question, first note that your total velocity is 2 m/s in the +x direction. The magnitude of your x-component is therefore 1 m/s, as you moved only 1 meter to the right.

Your y-component is also 1 m/s, as you remained stationary (the green arrow points in the same direction as the red one).

Final word on vector components and their uses

As you can see, the understanding of vector components is crucial to understanding physics. You should be able to tell what the x-, y-, and z-components of a vector represent and how to use them.

Component directions can be used in many physics situations, such as solving kinematic situations or working with angular velocity and acceleration.