Impulse is integral of force over time
======================================

*Impulse due to force* exerted on a body during collision is the measure of both the
magnitude and duration of the collision. Impulse can also be represented by a vector
by applying this law to the components of the force vector.

**Links:**

#. `Wikipedia, last formula in paragraph <https://en.wikipedia.org/wiki/Impulse_(physics)#>`__.

.. py:currentmodule:: symplyphysics.definitions.impulse_is_integral_of_force_over_time

.. py:data:: impulse

    Projection of :attr:`~symplyphysics.symbols.classical_mechanics.impulse` vector due to force :math:`\vec F`.

Symbol:
    :code:`J`

Latex:
    :math:`J`

Dimension:
    :code:`momentum`


.. py:data:: time

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

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: force

    Projection of :attr:`~symplyphysics.symbols.classical_mechanics.force` :math:`\vec F` as a function of time.

Symbol:
    :code:`F(t)`

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

Dimension:
    :code:`force`


.. py:data:: time_before

    Initial :attr:`~symplyphysics.symbols.basic.time` of collision.

Symbol:
    :code:`t_0`

Latex:
    :math:`t_{0}`

Dimension:
    :code:`time`


.. py:data:: time_after

    Final :attr:`~symplyphysics.symbols.basic.time` of collision.

Symbol:
    :code:`t_1`

Latex:
    :math:`t_{1}`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`J = Integral(F(t), (t, t_0, t_1))`


    Latex:
        .. math::
            J = \int\limits_{t_{0}}^{t_{1}} F{\left(t \right)}\, dt