Velocity is position vector derivative
======================================

Instantaneous **velocity** is the derivative of the body's position vector w.r.t. time.

**Notes:**

#. Also see :ref:`the scalar counterpart <Speed is distance derivative>` of this law.

**Links:**

#. `Wikipedia — Velocity <https://en.wikipedia.org/wiki/Velocity#Instantaneous_velocity>`__.

.. py:currentmodule:: symplyphysics.definitions.vector.velocity_is_position_vector_derivative

.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: velocity

    Vector of the body's velocity as a function of :attr:`~time`. Also see :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v(t)`

Latex:
    :math:`{\vec v} \left( t \right)`

Dimension:
    :code:`velocity`


.. py:data:: position_vector

    Vector of the body's position as a function of :attr:`~time`. Also see :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance`.

Symbol:
    :code:`d(t)`

Latex:
    :math:`{\vec d} \left( t \right)`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`v(t) = Derivative(d(t), t)`


    Latex:
        .. math::
            {\vec v} \left( t \right) = \frac{d}{d t} {\vec d} \left( t \right)