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Velocity :

 

In physics, velocity is defined as the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI (metric) system, it is measured in metres per second: (m/s) or ms-1. The scalar absolute value (magnitude) of velocity is speed. For example, "5 metres per second" is a scalar and not a vector, whereas "5 metres per second east" is a vector. The average velocity v of an object moving through a displacement velocity during a time interval (Δt) is described by the formula:

velocity

The rate of change of velocity is referred to as acceleration.

 

Equation on motion :

The instant velocity vector \, v of an object that has positions \, x(t) at time \, t and \, x(t + {\Delta t}) at time \, t +{\Delta t}, can be computed as the derivative of position:

\, \mathbf{v} = \lim_{\Delta t \to 0}{{\mathbf{x}(t+\Delta t)-\mathbf{x}(t)} \over \Delta t}={\mathrm{d}\mathbf{x} \over \mathrm{d}t}

The equation for an object's velocity can be obtained mathematically by evaluating the integral of the equation for its acceleration beginning from some initial period time \, t_0 to some point in time later \, t_n.

The final velocity v of an object which starts with velocity u and then accelerates at constant acceleration a for a period of time \, ( \Delta t) is:

\mathbf{v} = \mathbf{u} + \mathbf{a} \Delta t

The average velocity of an object undergoing constant acceleration is \begin{matrix} \frac {(\mathbf{u} + \mathbf{v})}{2} \; \end{matrix}, where u is the initial velocity and v is the final velocity. To find the displacement, x, of such an accelerating object during a time interval, Δt, then:

\Delta \mathbf{x} = \frac {( \mathbf{u} + \mathbf{v} )}{2}\Delta t

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

\Delta \mathbf{x} = \mathbf{u} \Delta t + \frac{1}{2}\mathbf{a} \Delta t^2,

can be used.

This can be expanded to give the position at any time t in the following way:

\mathbf{x}(t) = \mathbf{x}(0) + \Delta \mathbf{x} = \mathbf{x}(0) + \mathbf{u} \Delta t + \frac{1}{2}\mathbf{a} \Delta t^2,

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^2 = u^2 + 2a\Delta x.\,

The above equations are valid for both Newtonian mechanics and special relativity. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian 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. In other words only relative velocity can be calculated.

 

In Newtonian mechanics, the kinetic energy (energy of motion), \, E_{K}, of a moving object is linear with both its mass and the square of its velocity:

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

The kinetic energy is a scalar quantity.

 

Escape velocity is the minimum velocity a body must have in order to escape from the gravitational field of the earth. To escape from the earth's gravitational field an object must have greater kinetic energy than its gravitational potential energy. The value of the escape velocity from Earth is approximately 11100 m/s.

 

 

terms image Related Topics:

physics help image Escape Velocity

physics help image The Area Under the Velocity-Time Graph

 

terms image Related Flash Simulations:

physics help image Falling Velocity

physics help image Velocity and Acceleratoin

physics help image Relative Velocities

 

terms image Homework Problems:

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