Property:Acceleration

The rate at which an object's velocity changes with time. Has type accelerationwarning.pngUnsupported type "Acceleration" defined for property.

In formulae, typically has symbol a.

[edit] Definition

a = (Δ v) (Δ t)^-1 = (Δ r t^-1) (Δ t)^-1 = (Δ r) (Δ t)^-2

Where a is the average acceleration vector during the time interval Δ t, v is the Velocity vector, t is the time, and r is the position vector.

[edit] Semantic Relation

The semantic relation of acceleration is hard to express, because it's related to time and velocity. Velocity itself is related to position and time. The problem is that there are not related in a Class/Subclass manner (like in UML, RDF, OWL, ...), but in a mathematical one.

Therefore we need a mathematical relation model.

[[frac::((times::(delta, Velocity),(times::(delta, Time))]]

And also a simple T_EΧ like syntax.

[[=\frac{\delta \Velocity}{\delta \Time}]]

Also can be represented as a plain ascii expression as:

"a = delta(v)/delta(t)"  "(1)" ,

or "(= a (/ (delta v) (delta t)))"

can be derived from force equation as well:

"a = F/m" "(2)" ,

"(= a (/ F m))"

Where (v and t repeated for completeness):

v = Property:Velocity t = Property:Time F = Property:Force m = Property:Mass

Derivation of (1): delta(v)=a*delta(t) from Velocity -> a*delta(t) = delta(v) -> a = delta(v)/delta(t)

Derivation of <ask>Acceleration*</ask> :

<ask>Force*</ask><ask>Force*</ask> from Force -> m*a = F, -> a*m = F, -> a*m/m = F/m (by <ask>Equality*</ask> ), -> a*1 = F/m, -> <ask>Acceleration*</ask>

[edit] See also

• Math
• Units