nopeusvektoriin

Nopeusvektori (Finnish for velocity vector) is the vectorial representation of an object's rate of change of position with respect to time. It is defined mathematically as the derivative of the position vector with respect to time, v = d r / dt, where r denotes the position vector in a chosen coordinate system. In Cartesian coordinates the vector has components v = (vx, vy, vz), and its magnitude |v| equals the speed of the object. When expressed in polar or spherical coordinates the radial and angular components of the velocity can be derived from the corresponding position coordinates.

The notation for the velocity vector is typically the lowercase Latin letter v, often with a boldface or arrow notation to emphasize its vector nature. The magnitude of the velocity vector, called speed, is a scalar quantity given by |v| = sqrt(vx^2 + vy^2 + vz^2). The direction of the vector indicates the motion's trajectory. In physics, the velocity vector is used to calculate kinematic equations, determine momentum through p = m v, and describe dynamics via Newton's second law F = m a with acceleration a = d v / dt.

In special relativity, velocity is incorporated into the four-velocity, a Minkowski-space vector that couples temporal and spatial components under Lorentz transformations. The concept of velocity vector is ubiquitous across mechanics, electromagnetism, fluid dynamics, and general relativity, providing a concise way to capture both speed and direction of motion.