Let a particle travel a distance as a function of time (here, can be thought of as the Arc
Length of the curve traced out by the particle). The Speed (the Scalar Norm of the
Vector Velocity) is then given by

(1) |

(2) | |||

(3) | |||

(4) | |||

(5) | |||

(6) |

The Vector acceleration is given by

(7) |

Let a particle move along a straight Line so that the positions at times , , and are , ,
and , respectively. Then the particle is uniformly accelerated with acceleration Iff

(8) |

Consider the measurement of acceleration in a rotating reference frame. Apply the Rotation Operator

(9) |

(10) |

Grouping terms and using the definitions of the Velocity and Angular Velocity give the expression

(11) |

(12) | |||

(13) | |||

(14) |

a ``body'' acceleration, centrifugal acceleration, and Coriolis acceleration. Using these definitions finally gives

(15) |

**References**

Klamkin, M. S. ``Problem 1481.'' *Math. Mag.* **68**, 307, 1995.

Klamkin, M. S. ``A Characteristic of Constant Acceleration.'' Solution to Problem 1481. *Math. Mag.* **69**, 308, 1996.

© 1996-9

1999-05-25