# Acceleration

# Definition of acceleration

**Acceleration** can be defined as the **ability** of a body to move in a given unit of time. Since velocity is a magnitude that has a direction, so is **acceleration.**

The main concept of this definition comes **from Isaac Newton’s** studies of **mechanics** , through which it is determined that a specific object will be able to keep its movement in a uniform and rectilinear way. The **exception to the rule** occurs when an accelerating force acts on the given body.

This type of **acceleration** allows objects to increase or decrease their speed. If a certain object presents **changes** in a period of time, increasing or decreasing its acceleration in this way, it gives the option of being able to measure what is known as average speed, which is not more than the average considered of the accelerations at which it is submitted in that time range.

### Applicable formula

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

More precisely, dv and dt are defined as follows:

**dv = vf – vi** , where vf is the final velocity and vi, the initial velocity of the mobile. This difference indicates the direction of the acceleration.

**dt = tf – ti** , where tf is the final 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 an object of mass (m), and the acceleration (a) that it acquires. The formula that describes this relationship is Newton’s second law:

** F = ma from which it follows that a = F / m**

### Difference between velocity and acceleration

We must be clear that both concepts are totally different from each other. While speed is responsible for indicating the distance a body travels in a given period of time, acceleration is responsible for determining the variation of said speed in a unit of time.

### Examples of acceleration

- When a billiard ball is hit with the stick.
- Hitting a baseball with the bat.
- When a soccer ball is kicked.
- The speed of a train when braking until it reaches zero speed is known as negative acceleration.
- When an object is thrown from a high surface, its initial velocity will be zero and will increase as it falls thanks to the force of gravity. If the final velocity and the time it takes for the object to fall are determined, the acceleration of the object will be obtained.