Mathematics is present in several everyday situations, in Physics it has important applicability, as in Kinematics, which is the part of physics that studies movements, relating them through the concepts of position, velocity and acceleration. This relationship happens through the use of 1st and 2nd degree mathematical functions, let's fix our study on the 1st degree function degree, which is the foundation of uniform movements, those in which the velocity value is constant, that is, they do not have acceleration.
The 1st degree function has the following formation law: y = ax + b. One of the functions of uniform motion is given by the expression space versus time: s = s0 + vt. By comparing the two expressions, we build the following relationship: 
The comparison between the expressions makes it very clear that the formula defined as space versus time is a function of the 1st degree.
Example
Two cars move in a straight line in uniform motion and in the same direction. At the moment t0 = 0 they are 200 m apart as illustrated. If car A develops a constant speed of 8 m/s and car B of 6 m/s, how long does car A take to reach car B?
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Carriage A is part of the origin with a scalar velocity of 8 m/s, so the function of carriage A's movement is: s = s0 + vt → s = 0 + 8t → s = 8t
Carriage B starts from position 1000 meters with scalar speed 6 m/s, so the function of carriage B's movement is: s = 200 + 6t
The two cars are in the same direction, with car A's speed being greater than car B's speed, so at some point car A will catch up with car B. To calculate the instant of the encounter, it is enough to equalize the two functions. Then:
sTHE = SB
8t = 200 + 6t
8t - 6t = 200
2t = 200
t = 200/2
t = 100 s
After 100 seconds, or approximately 1.66 minutes, car A will catch up with car B.
by Mark Noah
Graduated in Mathematics
Brazil School Team
1st Degree Function - Roles - Math - Brazil School
Would you like to reference this text in a school or academic work? Look:
SILVA, Marcos Noé Pedro da. "Function of the 1st Degree in Kinematics"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/funcao-1-grau-na-cinematica.htm. Accessed on June 29, 2021.
