Velocity

:''This article is about velocity in physics. For other meanings, see velocity (disambiguation).'' Velocity (symbol: ''v'') is a vector (spatial) measurement of the rate and direction of motion. The scalar absolute value (Magnitude (mathematics)) of velocity is speed. Velocity can also be defined as rate of change of displacement (distance) or just as the rate of displacement, depending on how the term displacement is used. It is thus a vector quantity with dimension length/time. In SI units this is metre per second In mechanics the average speed v of an object moving a distance d during a time interval t is described by the simple formula: :

v = \frac{d}{t}

The instantaneous velocity vector v of an object whose position at time t is given by x(t) can be computed as the derivative :

v={\mathrm{d}x \over \mathrm{d}t} = \lim_{\Delta t \to 0}{\Delta x \over \Delta t}

Acceleration is the rate of change of an object's velocity over time. The average acceleration of a of an object whose speed changes from v_i to v_f during a time interval t is given by: :

a = \frac {( v_f - v_i )} {t}

Accelerating acceleration is the rate of change of an object's acceleration over time. However, an acceleration of accelerating acceleration would not be distinguished in practice as it would be experienced merely as a different slope of accelerating acceleration. The instantaneous acceleration vector a of an object whose position at time t is given by x(t) is :

\mathbf{a} = \frac {d\mathbf{v}} {dt} = \frac {d^2\mathbf{x}} {d t^2}

The final velocity v_f of an object which starts with velocity v_i and then accelerates at constant acceleration a for a period of time t is: :

v_f = v_i + a t

The average velocity of an object undergoing constant acceleration is (v_i + v_f)/2. To find the displacement d of such an accelerating object during a time interval t, substitute this expression into the first formula to get: :

d = t \times \frac { ( v_i + v_f )} {2}

When only the object's initial velocity is known, the expression :

d = v_i t + \frac {( a t^2 )} {2}

can be used. These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's Equation: :

v_f^2 = v_i^2 + 2 a d

The above equations are valid for both classical mechanics and special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical mechanics, all observers agree on the value of ''t'' and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. The kinetic energy (movement energy) of a moving object is linear with both its mass and the square of its velocity: :

E_{v} = \begin{matrix} \frac{1}{2} \end{matrix} mv^2

The kinetic energy is a scalar quantity. ==Polar coordinates== In connection with Coordinates (elementary mathematics), 2D velocity can be decomposed into radial velocity, away from or toward the origin, and transverse velocity, in the perpendicular direction, changing the direction of the body from the origin, and equal to the distance to the origin times the angular velocity. Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with a plus or minus to distinguish clockwise and anti-clockwise direction. If forces are in radial direction only, as in the case of a gravitational orbit, angular momentum is constant, hence transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant (Kepler%27s_laws_of_planetary_motion#Kepler.27s_second_law). Physical quantity Introductory physics la:Velocitas ms:Halaju simple:Velocity

Velocity

Question: If a particle has a defined position at every time, must it necessarily also have a defined velocity? Consider a particle moving along a line, so its position along the line at time t is x(t). Suppose we define x(t) as follows: { 1 if t > 0 x(t) = { { 0 if t <= 0 If I remember my calculus correctly, x'(0) is undefined, while x(t) = 0. Does it therefore follow that at time t=0, the particle has a position and is moving but has no velocity? Would it be physically possible (i.e. compatible with the laws of physics as we currently understand them) for a particle with that behaviour to actually exist? -- User:SJK ---- In classical (non-quantum) mechanics a particle with mass cannot make such an instantaneous jump in position. It implies infinite acceleration which implies infinite force. So this case is not physically possible in classical mechanics (assuming zero-mass particles are not physically possible). -- User:Eob the derivative of the step function x(t) you wrote above is the Dirac delta function. -- User:RAE ---- I am in browse mode tonight... but at some point mention will have to made of tangent spaces and tie the discussion back to :differential geometry. ---- Eob: What about in quantum mechanics? IIRC, quantum mechanics predicts instantaneous jumps in position (consider e.g. the Bohr model of the atom). And it has a zero-mass particle, the photon... -- User:SJK : I was not sure about quantum mechanics which was why I explicitly restricted my comments to classical mechanics. But now that I consider it more I would hazard that the question that was posed is not meaningful in quantum mechanics because you can never know x(t) exactly. As for the :The Bohr Model, it has been superceeded by a model of the atom surrounded by :orbitals which are standing waves of the wave function, so I am not sure it is relevant. --User:Eob

Velocity

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See other meanings of words starting from letter:

V

Words begining with Velocity:

Velocity
Velocity
Velocity
Velocity.png
Velocity5957
Velocityofsoundcover.jpg
Velocity_(disambiguation)
Velocity_(newspaper)
Velocity_(newspaper)
Velocity_(professional_wrestling)
Velocity_(software)
Velocity_Engine
Velocity_of_detonation
Velocity_of_light
Velocity_of_money
Velocity_of_Propagation
Velocity_of_propagation
Velocity_of_propagation
Velocity_of_Sound
Velocity_of_sound
Velocity_professional_wrestling
Velocity_sensitive
Velocity_Trap
Velocity_Trap
Velocity_trap
Velocity_trap