When you look at cars passing through the same street, you can see that they do not travel the same route in the same time frame.

The concept of speed, which is long before the invention of the car, arose from the need to express how quickly a piece of furniture describes a trajectory.

Consider, for example, the car in the illustration below. When it is at the 30 km milestone of a road, a timer is set and at that time zero time. When the timer indicates that 2 hours have passed, the car is in the 190 km milestone.

From the initial situation to the final situation, the mobile covered 160 km in 2h. Dividing 160 km by 2h we arrive at:

We then say that the average speed of the mobile over this time was 80 km / h (read “eighty kilometers per hour”)

Let's make a more general definition of speed from the figure below.

When the furniture occupies the position **Si** (the letter s indicates space and the index **i** indicates initial), the clock marks the time **you**. After a certain period of time, the car reaches the position **Sf** and the clock mark **tf** (the index** f** indicates final).

The subtraction Sf- Si corresponds to the displacement made (ie traveled), which will be represented by . The symbol (Greek capital letter delta) is used in mechanics to indicate variation. The subtraction tf - you, Represented by , corresponds to the time interval in which the mobile went from itself to sf. |

For a piece that describes a straight line (straight line) trajectory, the average velocity, **v**, is defined as:

In words:** The average speed of a piece of furniture over a certain period of time is equal to the distance the piece of furniture travels divided by the time interval.**

In equation: or

The unit used to express speed will depend on the units used for space and time.

If is in kilometers (Km) and in hours (h), the speed will be expressed in kilometers per hour (km / h). If is in meters (m) and in seconds (s) the speed will be expressed in meters per second (m / s). And so on. |

# Instantaneous velocity

We call instantaneous speed the speed with which a piece of furniture travels its path at any given moment. The speedometer of Brazilian vehicles express the instantaneous speed in km / h.

When the driver consults the speedometer of his car, he would drive in an hour if he kept the same speed all the time. However, a car rarely maintains a rigorously constant speed for an hour, or even much shorter intervals.

In a period of time where the driver maintains 80 km / h, the car will travel a greater distance than in another interval of the same duration, in which it maintains 60 km / h. The speed of a piece of furniture may or may not remain constant on a given route. This is the criterion that allows us to classify the movements, as we will see below.

## Let's classify the movements?

We already know that there are several types of movement. Think, in a roller coaster cart, for example, it speeds up, keeps its speed, loses speed, goes straight, turns around. Almost every movement around us is like this: quite varied!

We also already know that in order to study anything we have to establish a way of classifying it. Remember, for example, the classification of living things; There are several criteria for this classification.

Another example would be the books in a library. Ever wondered if no prior criteria were set for organizing books? It would be virtually impossible to find any copy. Our vision becomes broader and more organized when we have criteria for ranking. To classify movements, the criteria used are the shape of the trajectory and what is happening with velocity.

### Classification of movement by trajectory

If the path is straight, the motion will be **rectilinear**, if it is curved, the movement will be curvilinear. Here are some examples of moves **curvy**:

**Circular:**the trajectory is a circumference.**Parabolic:**the trajectory is a parable.**Elliptical:**the trajectory is an ellipse.

### Movement rating for speed variation

If the speed varies, we say that the movement is **miscellaneous**. On the contrary, if it remains constant, we say that the movement is **uniform**.

If the speed increases, we call the movement** accelerated**. If it decreases, it will be called braked or **retarded**.

There are some varied movements, where the speed value changes as time goes by, but in a completely predictable way. For example, when a body falls or is thrown near the earth's surface, its **speed is approximately 9.8 m / s** every second. As we have already seen, the magnitude that measures the change in velocity over time is acceleration. Therefore, for these movements, the average acceleration is:

This acceleration value is the same for all free-falling bodies on the Earth's surface in the same location. It is called acceleration of gravity and is symbolized by the letter g. For bodies close to the earth's surface, we will consider that the acceleration of gravity is equal to **10 m / s ^{2}**. In this way the acceleration will be constant and the velocity of the body will vary uniformly.

When a body falls under these conditions, its movement is uniformly accelerated rectilinear. And when it goes up, its movement is evenly retarded rectilinear.

Note that in the international system the unit for acceleration is the** m / s ^{2}.**