PlanetPhysics/Acceleration

The acceleration of an object is the time derivative of its velocity. Like velocity, acceleration can therefore be considered either as a vector quantity or as a 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). We can write the definition of acceleration (in vector form) as follows: $$ \mathbf{a}(t)\equiv\frac{\mathrm{d}\mathbf{v}(t)}{\mathrm{d}t}. $$

The SI unit of acceleration is $$\mathrm{m/s^2}$$ (metres per second per second, or metres per second squared). Another unit of acceleration is $$g$$, defined as $$g=9.80665\;\mathrm{m/s^2}$$; 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 $$\Delta\mathbf{v}$$ over a specified period of time $$\Delta\mathbf{t}$$, can also be defined: $$ \mathbf{\bar a}\equiv\frac{\Delta\mathbf{v}}{\Delta t}. $$

In classical mechanics, acceleration is caused by forces. If a total force $$\mathbf{F}$$ acts on an object with constant mass $$m$$, the object undergoes an acceleration $$\mathbf{a}$$ as described by Newton's second law: $$ \mathbf{F}=m\mathbf{a}. $$ In contrast to velocity, which depends on the observer's 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.