Defined as the change in velocity over a period of time. Acceleration is a vector quantity and therefore is stated as a quantity with a direction.

a = (v-u)/t (where a, v and u are vectors)

Where (using SI units):
a = acceleration of the body in metres per second per second (ms^-2, or metres per second squared)
v = final velocity of the body in metres per second (ms^-1)
u = initial velocity of the body in metres per second (ms^-1)
t = time period between the initial and final velocity, in seconds (s)

An accelerating body can also be decelerating (ie, negative acceleration) or be at rest. Also, instantaneous acceleration is a bit different.
1) A car that is travelling at 2ms^-1 changes its speed to 6ms^-1 over a period of five seconds, and doesn't change direction. During that five seconds, it had an average acceleration of .8ms^-2 in initial direction.

2) A car travelling forwards at 2ms^-1 is suddenly put into reverse and five seconds later it is travelling 2ms^-2 backwards. It's average acceleration is .8ms^-2 backwards (-.8ms^-2 forwards). Note in this example, the car would have been temporarily at rest just when it changes direction. It is still accelerating (in negative direction, ie backwards, ie decelerating) during this period.
by White Razor April 10, 2007
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Accelerate is a beautiful written dnf smut(dream not found) fanfic found on AO3.
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To increase the velocity of something. To speed something up. To step on the gas.
I hit the gas and I accelerate.
by 5'1"Racer December 27, 2005
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To speed(positive acceleration, aka acceleration) up slow down(Negative acceleration, aka deceleration)or change direction(aka turn)
I accelerated out of the street accelerated as i stopped at the light and accelerated as i turned the corner
by Daniel Cannon January 11, 2008
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When a man/woman is destined to break up with their partner and so by sleeping with them you simply accelerate the process, thus providing a useful service, you are then an accelerator.
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