Velocity

Velocity is a measurement of speed in a certain direction of motion. It is an important idea in kinematics, which is a part of classical mechanics that talks about how objects move. Because velocity tells us both how fast something is moving and in which direction, it is called a vector quantity.

The size of the velocity, or how fast something is moving without direction, is called speed. Speed is measured in metres per second in the SI system, which is the way scientists measure things around the world. For example, saying "5 metres per second" only tells us the speed, but "5 metres per second east" gives us both the speed and the direction, making it a velocity vector.

When an object's speed or direction changes, it is said to be accelerating. Understanding velocity helps scientists and engineers predict how things will move, from cars on the road to planets in space.

Definition

The average velocity of an object is how far it moves over a certain amount of time, divided by that time. For example, if a toy car moves 10 meters in 5 seconds, its average velocity is 2 meters per second.

The instantaneous velocity is the velocity of an object at one exact moment in time. It is like the speed you see on a speedometer at a specific instant.

Speed tells us how fast something is moving, but velocity tells us both how fast and in which direction it is moving. For example, a bicycle moving at 10 kilometers per hour north has a different velocity than the same bicycle moving at 10 kilometers per hour east, even though the speed is the same.

Velocity is measured in metres per second (m/s).

Equation of motion

Main article: Equation of motion

Velocity tells us how fast something is moving and in which direction. It is important for understanding motion.

Velocity is how quickly an object’s position changes over time. It includes both speed and direction. When we talk about average velocity, we mean the steady speed and direction that would give the same overall movement over a certain time.

Velocity can also be linked to acceleration, which is how quickly velocity changes. Special formulas help us connect velocity, time, and distance. These ideas work in both everyday physics and more advanced studies of motion.

Quantities that are dependent on velocity

Momentum

In physics, momentum is a property of moving objects. It depends on both the mass of the object and how fast it is moving. Momentum has both size and direction.

Kinetic energy

When an object moves, it has energy called kinetic energy. This energy depends on the object's mass and how fast it is moving. The faster the object moves, the more kinetic energy it has.

Drag (fluid resistance)

When an object moves through a fluid like air or water, it feels a force called drag. This force opposes the object's motion and depends on how fast the object is moving through the fluid.

Escape velocity

Escape velocity is the speed an object needs to leave a planet like Earth. This speed depends on the planet's mass and the distance from its center.

The Lorentz factor of special relativity

In the study of space and very fast speeds, scientists use a number called the Lorentz factor. This number changes depending on how close an object's speed is to the speed of light.

Relative velocity

Main article: Relative velocity

Relative velocity tells us how fast one object moves compared to another. This idea is important in physics because many situations involve more than one object moving.

Imagine two objects, A and B, moving. If we want to know how fast A is moving compared to B, we look at how their speeds and directions are different. In simple physics, this difference stays the same no matter where we measure it from. In more advanced physics, the result can change depending on where the viewer is standing.

Coordinate systems

Cartesian coordinates

In multi-dimensional Cartesian coordinate systems, velocity is split into parts that match each axis of the system. In a two-dimensional system, with an x-axis and a y-axis, the velocity parts are:

v x = d x / d t ,

v y = d y / d t .

The two-dimensional velocity is then v = ⟨ v x , v y ⟩. The size of this shows speed and is found by the distance formula.

In three-dimensional systems with an extra z-axis, the velocity part is:

v z = d z / d t .

The three-dimensional velocity is v = ⟨ v x , v y , v z ⟩ with its size also showing speed.

Polar coordinates

See also: Circular motion § In polar coordinates; and Radial, transverse, normal

In polar coordinates, a two-dimensional velocity is described by a radial velocity, which is the part of velocity away from or toward the start point, and a transverse velocity, which is perpendicular to the radial one. Both come from angular velocity, which is how fast something spins around the start point.

The radial and transverse speeds can be found from the Cartesian velocity and position. The transverse velocity is the part of velocity along a circle around the start point.

Angular momentum is the mass times the distance from the start point times the transverse velocity. If forces are only in the radial direction, like in a gravitational orbit, some special rules called Kepler's laws of planetary motion apply.