Velocity

Things move in many ways. Speed tells us how fast something goes.

But velocity is more. It is speed and a way. You might go fast to the east. That is a velocity.

If you change your way, you change your velocity. This is called acceleration. A car can turn in a circle. It has the same speed. But its velocity changes because it turns.

This is how we track motion.

How fast is something moving? People often use the word speed. Speed tells us how fast an object moves. But scientists use a different word: velocity.

Velocity is more than just speed. It includes speed and a direction. For example, you might move at 5 metres per second. That is a speed. But if you move 5 metres per second east, that is a velocity.

To have a constant velocity, you must move in a straight line. You must also keep the same speed. A car driving in a circle has a constant speed. However, its velocity changes because it turns. When velocity changes, we call it acceleration.

Velocity also helps us find other things. It helps us find momentum. Momentum is the mass of an object times its velocity. Velocity also helps us find kinetic energy. This is the power of a moving object. There is even something called escape velocity. This is the speed needed to leave a planet like Earth. On Earth, that speed is about 11,200 metres per second.

Velocity is a special way to measure motion. While many people use the word speed, scientists use velocity to be more exact. Speed only tells us how fast something is moving. Velocity is a vector quantity, which means it needs two parts. It needs a magnitude, which is the speed, and a direction. For example, moving at 5 metres per second is just a speed. But moving at 5 metres per second east is a velocity.

This distinction helps scientists describe exactly how objects move through space.

To understand how velocity works, we can look at how it changes. If an object changes its speed, its direction, or both, it is undergoing acceleration. For an object to have a constant velocity, it must move in a straight line. It must also keep the exact same speed the whole time. Imagine a car driving in a circle at 20 kilometres per hour. The car has a constant speed, but its velocity is changing. This happens because the car is constantly turning to stay in the circle.

Scientists use different math tools to find velocity. They can calculate average velocity over a period of time. This is done by taking the change in position and dividing it by the time. They can also find instantaneous velocity. This is the velocity at one exact moment in time. You can see this on a graph. On a velocity versus time graph, the area under the curve shows the displacement. Displacement is the change in an object's position.

There are many important facts about how velocity affects the world. Velocity is used to calculate momentum, which is mass times velocity. It also helps find kinetic energy, the energy of a moving object. Velocity even helps us understand how objects move through fluids like air or water. This is called drag, and it depends on the square of the velocity. There is also escape velocity. This is the minimum speed an object needs to leave a huge body like Earth.

On Earth's surface, that speed is about 11,200 metres per second.

Velocity connects to many things you might already know. You can see velocity in how cars move on a road. You can also see it in how planets move in space. In a coordinate system, like a map, velocity can be broken into parts. We use x, y, and z axes to show direction in three dimensions. Scientists also use polar coordinates to show motion in a circle. This includes radial velocity, which moves toward or away from a center. It also includes transverse velocity, which moves around the center.

Velocity is a fundamental concept in kinematics, which is the branch of classical mechanics describing how physical objects move. While people often use "speed" and "velocity" to mean the same thing, they are scientifically different. Velocity is a vector quantity, meaning it requires both a magnitude and a direction to be fully defined. The magnitude of velocity is simply the speed of the object. For example, saying an object moves at 5 metres per second is a scalar measurement of speed. However, saying it moves at 5 metres per second east provides a velocity.

To understand how velocity works, we must look at how it changes over time. If an object changes its speed, its direction, or both, it is undergoing acceleration. For an object to maintain a constant velocity, it must move in a straight line at a constant speed. If a car travels at 20 kilometres per hour in a circular path, its speed remains constant. However, its velocity is changing because its direction is constantly shifting. This change in direction means the car is technically accelerating.

Scientists use several mathematical methods to calculate different types of velocity. Average velocity is the change in an object's position divided by the duration of a specific time period. This represents the constant velocity that would produce the same displacement as a variable velocity. In contrast, instantaneous velocity is the velocity of an object at one specific moment. Mathematically, this is the limit of the average velocity as the time interval approaches zero. On a velocity versus time graph, the instantaneous velocity can be seen as the slope of the tangent line at any point.

Velocity is also deeply connected to the concept of displacement. In calculus, the integral of a velocity function represents the displacement function. This means that on a velocity versus time graph, the area under the curve represents the object's displacement. Displacement is different from distance because it measures the change in position. While distance always increases as an object moves, displacement can increase, decrease, or even become zero if an object returns to its starting point. Consequently, the magnitude of average velocity is always less than or equal to the average speed.

Many other physical properties depend directly on an object's velocity. In classical mechanics, momentum is defined as the product of an object's mass and its velocity. Kinetic energy, which is the energy an object possesses due to its motion, also depends on velocity. Specifically, kinetic energy is a scalar quantity that depends on the square of the velocity. Furthermore, velocity affects how objects move through fluids, such as air or water. This resistance is called drag, and the drag force is dependent on the square of the object's velocity.

In the study of space and gravity, velocity reaches extreme importance through escape velocity. Escape velocity is the minimum speed a ballistic object needs to break free from the gravitational pull of a massive body like Earth. To achieve this, the object's kinetic energy must balance its gravitational potential energy. On the surface of the Earth, the escape velocity is approximately 11,200 metres per second. Interestingly, this value is independent of the direction the object is launched, as long as it does not hit something in its path.

Finally, velocity can be analyzed using different coordinate systems to describe motion in space. In a Cartesian coordinate system, velocity is broken into components along the x, y, and z axes. In two dimensions, the velocity vector is composed of x and y components. In three-dimensional systems, a z-axis component is added. Scientists also use polar coordinates to describe motion around a central point. This involves radial velocity, which moves toward or away from the center, and transverse velocity, which moves perpendicular to the radial direction.