Acceleration
Let a particle travel a distance 
as a function of time 
(here, 
can be thought of as the ArcLength 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) |
is the Unit Tangent Vector, 
the Curvature, the Arc Length, and 
the Unit Normal Vector.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 AngularVelocity 
give the expression | (11) |
 | |  | (12) |
 | |  | (13) |
 | |  | (14) |
a ``body'' acceleration, centrifugal acceleration,
andCoriolis acceleration. Using these definitions finally gives | (15) |
). Thecentrifugal acceleration is familiar to riders of merry-go-rounds, and theCoriolis acceleration is responsible for the motions of hurricanes onEarth 
and necessitates large trajectory corrections for intercontinental ballistic missiles.See also Angular Acceleration, Arc Length, Jerk, Velocity
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.
- Hereditary Representation
- Heredity
- Hermann Grid Illusion
- Hermann-Hering Illusion
- Hermann-Mauguin Symbol
- Hermann's Formula
- Hermite Constants
- Hermite Differential Equation
- Hermite-Gauss Quadrature
- Hermite Interpolation
- Hermite-Lindemann Theorem
- Hermite Polynomial
- Hermite Quadrature
- Hermite's Interpolating Polynomial
- Hermite's Theorem
- Hermitian Form
- Hermitian Matrix
- Hermitian Operator
- Hermit Point
- Heronian Tetrahedron
- Heronian Triangle
- Heron's Formula
- Heron Triangle
- Herschel
- Herschfeld's Convergence Theorem