# Rectilineal movement

Rectilinear motion, motion whose path is a straight line. If the mobile does not change direction, the only variation that speed can experience is that of its module. This allows rectilinear motion to be classified into rectilinear and uniform motion, if the modulus of velocity does not vary, and rectilinear motion uniformly varied if the modulus of velocity varies steadily over time. If the rectilinear movement is considered to take place in a single dimension, the position of the mobile at any instant is determined by the module of the position vector.

Summary

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• 1 Rectilinear and uniform movement
• 1 Graphics of an MRU
• 2 Uniformly varied rectilinear motion
• 1 Graphics of an MRUV
• 4 Sources

Straight and smooth movement

This movement is characterized in that its trajectory is a straight line and the modulus, direction and direction of speed remain constant over time. Consequently, there is no acceleration , since the tangential acceleration is zero, since the modulus of the velocity is constant, and the normal acceleration is null because the direction of the velocity is constant. The position equation for a mobile moving in a rectilinear and uniform motion with a speed v is:

x = x 0 + v · t

where x 0 is the position of the mobile at the initial instant. Therefore, the mobile travels through equal spaces in equal times.

Graphics of an MRU

The graph of position versus time in uniform rectilinear motion is a line whose slope is velocity:

The graph of velocity versus time in uniform rectilinear motion is a horizontal line:

Uniformly varied rectilinear motion

Uniformly varied rectilinear motion is characterized by its trajectory being a straight line and the modulus of velocity varying proportionally with time. Therefore, the normal acceleration is null because the speed does not change direction and the tangential acceleration is constant, since the modulus of the speed varies uniformly with time. This movement can be accelerated if the velocity modulus increases as time elapses and delayed if the velocity modulus decreases over time. The equation of the speed of a mobile moving with a uniformly varied rectilinear motion with an acceleration a is:

v = v 0 + a · t

where v 0 is the speed of the mobile at the initial instant. Therefore, speed increases equal amounts in equal times. The position equation is:

x = x 0 + v 0 · t + ½ · a · t 2

A particular case of uniformly varied rectilinear motion is that acquired by bodies falling freely or being thrown towards the surface of the Earth, or being thrown upwards, and the equations of speed and position are the above, in which the acceleration, a, is replaced by the acceleration of gravity, g.