Rectilineal movement
Rectilinear Movement is a movement whose trajectory is a straight line. If the mobile does not change direction, the only variation that the speed can experience is that of its module. This allows rectilinear motion to be classified into rectilinear and uniform motion, if the magnitude of the velocity does not vary, and uniformly varied rectilinear motion if the magnitude of the velocity varies constantly over time. If it is considered that the rectilinear movement takes place in a single dimension, the position of the mobile at any instant is determined by the magnitude of the position vector.
Summary
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- 1 Rectilinear and uniform movement
- 1 Graphs of an MRU
- 2 Uniformly varied rectilinear motion
- 1 Graphs of an MRUV
- 3 See also
- 4 Sources
Rectilinear and uniform movement
This movement is characterized because its trajectory is a straight line and the module, direction and direction of the speed remain constant over time. Consequently, there is no acceleration , since the tangential acceleration is zero, since the magnitude of the velocity is constant, and the normal acceleration is zero because the direction of the velocity is constant. The equation of position for a mobile that moves with a rectilinear and uniform movement 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 as a function of time in a uniform rectilinear motion is a line whose slope is the velocity:
The graph of velocity as a function of time in a uniform rectilinear motion is a horizontal line:
Uniformly varied rectilinear motion
Uniformly varied rectilinear motion is characterized because its trajectory is a straight line and the magnitude of the velocity varies proportionally to time. Consequently, the normal acceleration is zero because the velocity does not change direction and the tangential acceleration is constant, since the magnitude of the velocity varies uniformly with time. This movement can be accelerated if the magnitude of the velocity increases as time passes and retarded if the magnitude of the velocity decreases over time. The equation for 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 by 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 when falling freely or when thrown towards the surface of the Earth, or when thrown upwards, and the equations of velocity and position are as above, in which the acceleration, a, is replaced by the acceleration of gravity, g.