# Acceleration – Concept, formula and examples

We explain what acceleration is and the formulas used to calculate it. Also, its difference with speed and examples.

## What is acceleration?

The acceleration of an object is a magnitude that indicates how the velocity of the object changes in a unit of time. Since velocity is a vector quantity (that is, it has a direction), acceleration is also a vector quantity. It is usually represented by the sign to and its unit of measure in the International system is m / s2 (meters per second squared).

The origin of acceleration as a concept comes from Isaac Newton’s studies of mechanics (founder of classical mechanics), in which it is ensured that an object will retain its rectilinear and uniform motion (MRU) unless forces that lead to acceleration act on it.

These forces can produce accelerations that cause objects to increase or decrease their speeds. It is important to note that when working with vectors, it is essential to define directions. If, for example, we define east as the positive direction of motion, then a positive acceleration always implies an increase in velocity. However, a negative acceleration may indicate a decrease in speed in the east direction, or an increase in speed in the west direction.

If an object experiences changes in its acceleration in a certain period of time, then what is defined as “average acceleration” can be calculated, which is the average of the accelerations it undergoes in that time range.

## Acceleration formula

Classical mechanics understands acceleration as a variation of the velocity of a body in time. Mathematically this is written as: a = dv / dt, where to is acceleration, dv the difference in speeds and dt the time at which the acceleration occurs.

More precisely, dv and dt are defined as follows:

• dv = vF – vi, where vF is the final speed and vi, the initial velocity of the mobile. This difference indicates the direction of the acceleration.
• dt = tF – ti, where tF is the end time and ti the initial time of the movement. Unless otherwise stated, the starting time is usually taken as 0 seconds.

On the other hand, there is a proportional relationship between the force (F) that is applied to a mass object (m), and acceleration (to) that you acquire. The formula that describes this relationship is Newton’s second law:

• F = ma from where it follows that a = F / m

## Speed ​​and acceleration

Speed ​​and acceleration they are two different concepts. Velocity indicates the amount of distance that a body travels in a unit of time (that is why it has units of m / s, for example), while acceleration is the variation of said velocity in a unit of time (and that is why it has units of m / s2, for instance).

## Examples of acceleration

• A billiard ball accelerates when struck with the cue. Knowing the force provided by the cue and the mass of the ball, we can obtain its acceleration.
• If we know the speed of a train just before it starts to brake and the time it takes to reach zero speed, then we can calculate its declension (negative acceleration).
• An object is thrown from a balcony (then its initial speed is zero) and due to the force of gravity, it will fall with a speed that will increase until it is maximum on the floor. If we know this final speed and the time it takes to fall, we can obtain the acceleration (which will be that of gravity).