Understanding Uniform Rectilinear Motion: Concepts and Equations

Classified in Physics

Written at February 14, 2025 on English with a size of 4.39 KB.

Uniform Rectilinear Motion

A rectilinear movement is when an object is described as moving in a straight path, and is uniform when its speed is constant over time, as its acceleration is zero. We refer to it by the acronym MRU.

The MRU is characterized by:

Movement is done on a straight line.
Velocity is constant, involving constant magnitude and direction.
The magnitude of velocity is called speed.
Zero acceleration.

Kinematics (Greek κίνημα, Kine, movement) is the branch of classical mechanics that studies the laws of motion of bodies without regard to the causes that produce it, limited essentially to the study of time-dependent trajectory.

Uniformly Accelerated Rectilinear Motion

In this motion, the acceleration is constant, so the mobile speed and position vary linearly with time quadratically. The equations governing this motion are:

$a = a_0 = \text (const.) \,$

$x = x_0 + v_0 t + \frac (1) (2) at ^ 2$

Free-fall is the motion of a body under the exclusive action of a gravitational field. Although this formal definition excludes the influence of other forces such as aerodynamic drag, often they must be taken into account when the phenomenon occurs within a fluid, like air or other fluid. The concept is applicable even to moving objects upwardly decelerating under the action of gravity.

Equation of Motion

By Newton's second law, force $\mathbf (F)$ acting on a body equals the product of its mass $m \,$ by the acceleration it acquires. In free fall involving only the weight $\mathbf (P)$ (vertically downwards) and the aerodynamic drag $\mathbf (f) (v)$ in the same direction, and opposite to the velocity. Within an approximately constant gravitational field, the equation of motion of free fall is:

$\ mathbf (F) = \ mathbf (P) + \ mathbf (f) =-mg (\ mathbf (j)) - f \ frac (\ mathbf (v)) (v) = m \ frac (d \ mathbf ( v)) (dt)$

According to Newton's 1st Law, every particle remains at rest or in uniform rectilinear motion when there is no net force acting on the body.

This is an ideal situation, since there are always forces that tend to alter the motion of particles. The movement is inherent and can be said to be linked as part of matter itself.

Since we can not really say that some object is at complete rest.

The MRU is characterized by:

a) Movement is performed in a single direction in the horizontal axis.

b) Constant speed, direction, and magnitude implies unchanged velocity.

c) The magnitude of velocity is called speed. This movement has no acceleration (acceleration = 0).

MRU Mathematical Relationship:

The concept of velocity is the change of position (displacement) with respect to time.

Formula:

v = d / t d = v * t t = d / v

v = velocity d = distance or travel time t = time

Uniform Linear Motion

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