# PesWiki.com

## PowerPedia:Velocity

Lasted edited by Andrew Munsey, updated on June 15, 2016 at 1:44 am.

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The velocity of an object is simply its There was an error working with the wiki: Code[1], both speed and direction are required to define it.

#### Explanation

The velocity (v) is a physical quantity of an object's motion.

Velocity is speed that has direction.

The average velocity (v) of an object moving a distance (d) in a straight line during a time interval (t) is described by the formula:

v = \frac{d}{t}

The There was an error working with the wiki: Code[13] (in the same direction as the velocity) can be found by taking the area under the graph or the There was an error working with the wiki: Code[14].

#### Formal description

Velocity (symbol: v) is a There was an error working with the wiki: Code[2] measurement of the rate of change of displacement from a fixed point. The There was an error working with the wiki: Code[3] There was an error working with the wiki: Code[4]) of velocity is There was an error working with the wiki: Code[5] or just as the rate of There was an error working with the wiki: Code[15].

It is a vector quantity with dimension LT(-1). In. the SI (metric) system it is measured in There was an error working with the wiki: Code[16].

The instantaneous velocity vector (v) of an object that has position at time (t) is given by x(t) can be computed as the There was an error working with the wiki: Code[17]:

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

The equation for an object's velocity can be obtained mathematically by taking the There was an error working with the wiki: Code[18] 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 v2 of an object which starts with velocity v1 and then accelerates at constant acceleration a for a period of time t is:

:v_2 = v_1 + at\\!.

The average velocity of an object undergoing constant acceleration is \frac {(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_1 + v_2 )}{2}.

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

:d = v_1 t + \frac{1}{2}a t^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 There was an error working with the wiki: Code[19]:

The above equations are valid for both There was an error working with the wiki: Code[20] and There was an error working with the wiki: Code[21]. Where There was an error working with the wiki: Code[20] and There was an error working with the wiki: Code[21] differ is in how different observers would describe the same situation. In particular, in There was an error working with the wiki: Code[20], 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 There was an error working with the wiki: Code[25]. In other words only There was an error working with the wiki: Code[26] can be calculated.

The Kinetic energy (Energy of motion) of a moving object is linear with both its Mass and the square of its velocity:

:E_{v} = \frac{1}{2} mv^2.

The kinetic energy is a There was an error working with the wiki: Code[6] quantity.

#### Polar coordinates

In There was an error working with the wiki: Code[7], a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin, and There was an error working with the wiki: Code[27] velocity, the component of velocity along a circle centred at the origin, and equal to the distance to the origin times the There was an error working with the wiki: Code[28].

There was an error working with the wiki: Code[29] 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 the radial direction only, as in the case of a gravitational There was an error working with the wiki: Code[30], angular momentum is constant, and 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. These relations are known as There was an error working with the wiki: Code[31].

#### Related concepts

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#### External articles and references

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.