PlanetPhysics/Acceleration

The acceleration of an [[../TrivialGroupoid/|object]] is the time derivative of its velocity. Like velocity, acceleration can therefore be considered either as a [[../Vectors/|vector]] quantity or as a [[../Vectors/|scalar]] quantity. Acceleration is usually denoted by the symbol $a$, by $\dot{v}$ (the time derivative of the velocity) or by $\ddot{x}$ (the second time derivative of the [[../Position/|position]]). We can write the definition of acceleration (in vector form) as follows: $𝐚(t)\equiv \frac{\mathrm{d}𝐯(t)}{\mathrm{d}t}.$

The SI unit of acceleration is $\mathrm{m}/{\mathrm{s}}^{\mathrm{2}}$ (metres per second per second, or metres per second squared). Another unit of acceleration is $g$, defined as $g=9.80665\mathrm{m}/{\mathrm{s}}^{\mathrm{2}}$; this is approximately the acceleration due to gravity at the surface of the Earth at a latitude of $45^{\circ }$.

In addition to acceleration as the time derivative (instantaneous rate of change) of velocity, the average acceleration , or the change of velocity $\mathrm{\Delta }𝐯$ over a specified period of time $\mathrm{\Delta }𝐭$, can also be defined: $\overline{𝐚}\equiv \frac{\mathrm{\Delta }𝐯}{\mathrm{\Delta }t}.$

In [[../MathematicalFoundationsOfQuantumTheories/|classical mechanics]], acceleration is caused by forces. If a total force $𝐅$ acts on an object with constant [[../Mass/|mass]] $m$, the object undergoes an acceleration $𝐚$ as described by Newton's second law: $𝐅=m𝐚.$ In contrast to velocity, which depends on the observer's [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|system]] of reference, acceleration can be called an absolute quantity, in the sense that two observers moving with constant velocity with respect to each other perceive the same acceleration.