# Calculations

distance (s) | <= | |

time (t) | <= | |

velocity (V) | => |

# Some facts

- Velocity is a vector size.
- It specifies the
**change of the position vector**in time. The concept of velocity was formalized with the development of calculus. Since then, the velocity is defined as the**position vector derivative with time**i.e.:

$\vec{v} = \dfrac{\vec{dr}}{dt}$where:

- $\vec{v}$ is velocity vector,

- $\vec{r}$ is position vector,

- $t$ is time.

- $\vec{v}$ is velocity vector,
- In common parlance - when we use the word speed - we normally refer to
**the scalar size**, representing the value of the velocity vector (its "length"). - The velocity by definition only applies to singl point in time. Sometimes, in order to emphasize this fact (and rule out a possible confusion with the average speed) it is called
**instantaneous velocity**. - There is also concept of
**average velocity**, which is**ratio of distance to time**, in which this distance has been traveled. - Average velocity is sometimes colloquially called
**speed**, but it is not a phrase used by physicists. - The basic unit of velocity in the SI system is
**meter per second**:

$\dfrac{m}{s}$ - According to
**Einstein's theory of relativity**the highest attainable speed in nature is**the speed of light**amounting to 299 792 458 m/s.

- The speed of light constant exists in many physical formulas e.g. equation desribing
**the equivalence of energy and mass:**

$E=mc^2$

**Einstein's special theory of relativity**gives a more general sense of the speed of light as**limit velocity of energy transport**(or otherwise velocity of impact) in the universe..

- The light is electromagnetic wave with the frequency that is visible to the human eye. However, the speed of light concerns to all of electromagnetic waves and does not depend on their frequency. This means that for example radio or wifi signals are transmited with the speed of light.

- The speed of light constant exists in many physical formulas e.g. equation desribing
- Other common velocity constants are for example:

- First cosmic velocity - the smallest horizontal velocity to be given to the body relative to the celestial body attracts them to the body is moved along a closed orbit. In other words, it is the speed needed to
**became a satellite**.

- Second cosmic velocity - the velocity needed to "break free" from the
**gravitational attraction of the given orb**(for example Earth)..

- Third cosmic velocity - the initial velocity which a body has to have to
**leave the Solar System**.

- Fourth cosmic velocity - the initial velocity needed to
**leave the Milky Way**.

- First cosmic velocity - the smallest horizontal velocity to be given to the body relative to the celestial body attracts them to the body is moved along a closed orbit. In other words, it is the speed needed to

# Average velocity formula:

$v = \dfrac{s}{t}$

where:- p - average velocity

- s - distance
- t - time

# Average velocity formula solved for distance:

$s = v \times t$

# Average velocity formula solved for time:

$t = \dfrac{s}{v}$

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# Ancient version of this site - links

In December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.

Direct link to the old version: "Calculla v1" version of this calculator

Direct link to the old version: "Calculla v1" version of this calculator