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Velocity is the speed in combination with the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it.
The most common form of the transformation, parametrized by the real constant , representing a velocity confined to the x-direction, is expressed as [1] [2] ′ = ′ = ′ = ′ = where (t, x, y, z) and (t′, x′, y′, z′) are the coordinates of an event in two frames with the spatial origins coinciding at t = t′ =0, where the primed ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The Lorentz transformation: The simplest case is a boost in the x-direction (more general forms including arbitrary directions and rotations not listed here), which describes how spacetime coordinates change from one inertial frame using coordinates (x, y, z, t) to another (x ′, y ′, z ′, t ′) with relative velocity v: ′ = (), ′ = ().
The special theory of relativity, formulated in 1905 by Albert Einstein, implies that addition of velocities does not behave in accordance with simple vector addition.. In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light.
To evaluate the velocity, the derivative of the unit vector u ρ is needed. Because u ρ is a unit vector, its magnitude is fixed, and it can change only in direction, that is, its change du ρ has a component only perpendicular to u ρ. When the trajectory r(t) rotates an amount dθ, u ρ, which points in the same direction as r(t), also ...
is the drag force, which is by definition the force component in the direction of the flow velocity, is the mass density of the fluid, [1] is the flow velocity relative to the object, is the reference area, and
Top: frame F′ moves at velocity v along the x-axis of frame F. Bottom: frame F moves at velocity −v along the x′-axis of frame F′. [5] The invariant interval can be seen as a non-positive definite distance function on spacetime. The set of transformations sought must leave this distance invariant.