Let's start with and assume that acceleration is constant.

(1) |

Therefor we can write the above relationship in a different form:

(2) |

Finally we arrive at:

(3) |

Note that

(4) |

so we can write:

(5) |

(6) |

If we let be velocity and be position we can write the
following set of coupled differential equations:

(7) |

State Equation:

(8) |

Observation Equation:

(9) |