Acceleration is the rate at which the velocity of an object changes with respect to time. In other words, acceleration can be thought of as how fast velocity changes. Acceleration has units of velocity over time. In the International System of Units (SI), acceleration is measured in units of meters per second squared .
Velocity takes both speed and direction into account. It is a relatively common misconception that accelerating means that an object is speeding up, but this is not necessarily true. An object traveling in a straight line is accelerating regardless of whether it is speeding up or slowing down, since its velocity is changing. Also, it is possible for an object to be accelerating even if it maintains a constant speed, as long as the direction of the object is also constantly changing. One such example is movement around a circle at constant speed. Even though the speed is not changing, the direction always is, and the object is therefore accelerating.
Another common misconception is that a large velocity corresponds to a large acceleration. This is not true. Acceleration is the rate of change of the velocity of an object. If an object has a constant velocity (constant speed and constant direction) then its acceleration is 0, no matter how large the velocity is.
Acceleration vs deceleration
Deceleration is defined as acceleration in the direction opposite of the velocity. It is most commonly used in regards to a vehicle or object slowing down. Mathematically, deceleration is negative acceleration based on the fact that the positive direction is defined as the direction that the object was moving in.
However, it is worth noting that not all negative acceleration results in an object slowing down. Remember that acceleration (like velocity) has a directional component. The positive and negative directions need to be defined. If, for example, we are given a negative acceleration, and the object is already moving in the negative direction, the negative acceleration will result in the object speeding up in the negative direction. On the other hand, if the object is moving in the negative direction and undergoes positive acceleration, it will slow down.
The figure above shows a vector that represents a velocity. The positive direction is defined to the right of the page and the negative to the left. Above in blue, another vector represents a positive acceleration, that if applied to the velocity, will increase the velocity of the object. The negative acceleration, shown in red below, does the opposite. If the velocity vector pointed left instead, the negative acceleration would increase the velocity and the positive acceleration would decrease it.