# Velocity is a vector quantity

speed of a body can be defined as the distance that this very body travels per unit of time. In the SI system, it is measured in m/s (meters per second). However, in physics, velocity is considered as the distance that a body travels **in a certain direction** per unit of time. Since the direction is indicated, the velocity becomes a vector quantity.

Also, often in physics, the concept of “velocity” is replaced by a “velocity vector”. However, often in Russian language, simply “velocity” is understood as a vector value. In English, there are two concepts of velocity: velocity – velocity as a vector quantity, speed – speed as a scalar quantity, denoting the speed of movement.

To indicate the movement of a body per unit of time (that is, its velocity), it is necessary to show 1) how much the body has moved per unit of time and 2) in which direction.

On the graphs of the dependence of the coordinate of the body on time, not only the speed of the body is reflected, but also the direction of the speed of the body. So, if the coordinate increases over time, then the body moves in a positive direction. If the coordinate decreases over time, then the body moves in the negative direction. In the first case, the velocity will be a positive value, in the second negative. Thus and from here it follows that velocity is a vector quantity.

For rectilinear uniform motion, the coordinate (x) of the body at time t is determined by the formula x = x_{0} + vt. Here x_{0} is the coordinate of the body at the time of the beginning of measurement (t_{0}), v is the speed of the body, that is, its movement in 1 unit of time (usually a second). If the body moves in the negative direction of the x-axis, then the velocity will have a negative value, and then the formula will take the form x = x_{0} – vt.

Below in the coordinate system are graphs of the movement of three bodies. Graphs show how the coordinates of bodies have changed over time. The body, whose graph is depicted in green, moved in the positive direction of the x-axis (which is depicted vertically), since the more seconds passed, the greater the x-coordinate of the body. The same can be said about the movement of the body, whose schedule is blue. The orange graph shows that the body moved in the negative direction of the x-axis (vertically downward), as with each subsequent second of movement, its coordinate decreased.

The “blue” body moved faster than the “green”, since its graph has a steeper rise, that is, the coordinate changed more with each passing second. This can be seen in the formulas. One body has v = 2 m/s, the other has v = 4 m/s. The vector velocity of the “orange” body is -1 m/s. Minus says that it moved in the opposite positive direction. The speed modulus is 1 m/s.

A minus before the numerical velocity value does not mean that the body moves more slowly than one that has a plus. So a body that has a velocity vector of -10 m / s moves faster than a body whose speed is 9 m / s. Minus reflects only that the body is moving in the opposite direction.

The fact that speed in physics is taken as a vector quantity is, among other things, a consequence of the fact that, depending on the direction of motion, the change in the coordinate of the body on the graph can be both positive and negative. The change in coordinate is as the difference between the next and previous point in time. If, for example, the body at a time after 5 s from the beginning of the measurement was at a point with a coordinate of 12 m, and after 6 s – at a point with a coordinate of 16 m, then the change is 16 – 12 = 4 m (the value is positive). If the body was first at a point of 12 m, and then 8 m, then 8 – 12 = -4 m (the value is negative).