The vector displacement of the body is given by

(43) |

(44) |

(45) | |||

(46) | |||

(47) |

Thus, the -component of velocity is simply the time derivative of the -coordinate, and so on.

By analogy with the 1-dimensional equation (16), the body's
vector acceleration
is simply the *derivative* of with respect to
. In other words,

(48) |

(49) | |||

(50) | |||

(51) |

Thus, the -component of acceleration is simply the time derivative of the -component of velocity, and so on.

As an example, suppose that the coordinates of the body are given by

(52) | |||

(53) | |||

(54) |

The corresponding components of the body's velocity are then simply

(55) | |||

(56) | |||

(57) |

whilst the components of the body's acceleration are given by

(58) | |||

(59) | |||

(60) |