Acceleration is the rate of change of velocity.
At any point on a speed-time graph, the magnitude of the acceleration is given by the gradient of the tangent to the curve at that point.
In physics, acceleration is defined as the rate of change of velocity, or as the second derivative of position (with respect to time). It is then a vector quantity with dimension length/time². In SI units, acceleration is measured in meters/second² (m·s-2). The term acceleration generally refers to the rate of change in instantaneous velocity. (velocity is speed and direction)
In common speech, the term acceleration is only used for an increase in speed;
a decrease in speed is called deceleration.
In physics, any increase or decrease in speed is referred to as acceleration and similarly,
motion in a circle at constant speed is also an acceleration, since the direction component of the velocity is changing.
After completing his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant proper acceleration are indistinguishable from those in a gravitational field. This was the basis for his development of general relativity, a relativistic theory of gravity.
This is also the basis for the popular Twin paradox, which asks why one twin ages less when moving away from his sibling at near light-speed and then returning, since the non-aging twin can say that it is the other twin that was moving.
General relativity solved the why does only one object feel accelerated? problem which had plagued philosophers and scientists since Newton's time
(and caused Newton to endorse absolute space).
In special relativity, only inertial frames of reference (non-accelerated frames) can be used and are equivalent;
general relativity considers all frames, even accelerated ones, to be equivalent.