Curso de Física. Tema 1: Movimiento. 1.1 Movimiento en 1D

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This section introduces the topic of motion in one dimension, defining movement and the concept of a reference system.

Understanding Movement in One Dimension

• Movement is defined as the change in position of an object over time, simplifying objects to points for mathematical ease.

• Introducing the concept of a reference system, crucial in physics to specify an object's motion relative to a chosen origin.

• Differentiating between movements in one, two, and three dimensions impacts the mathematical complexity involved.

• Examples illustrate movements: a car moving horizontally (1D), a ball following a parabolic path (2D), and a fly moving freely in space (3D).

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Delving into the significance of describing motion mathematically based on dimensions.

Mathematical Description of Motion

• Describing motion in one dimension is simpler due to not requiring vector treatment compared to two or three dimensions.

• Textbooks often separate discussions on 1D from 2D/3D motions due to increased complexity with vectors.

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Defining key concepts related to motion in one dimension such as position and displacement.

Key Concepts: Position and Displacement

• Position refers to an object's location concerning a coordinate origin at any given time denoted by 'x'.

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In this section, the concept of velocity is introduced, distinguishing between average and instantaneous velocity. The relationship between displacement, time, and speed is explained using examples.

Velocity Concepts

• Average velocity is calculated by dividing total distance traveled by total time taken.

• Instantaneous velocity refers to the speed at a specific moment in time.

• Instantaneous velocity is determined by applying the concept of average velocity over increasingly smaller time intervals, approaching zero.

• Instantaneous velocity can also be defined as the derivative of position with respect to time.

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This part delves into acceleration, defining it as the rate of change of velocity over time. The distinction between average and instantaneous acceleration is discussed along with their mathematical expressions.

Acceleration Definition

• Acceleration measures how a body's speed changes over time.

• Average acceleration is calculated as the change in velocity divided by the time interval.

• Instantaneous acceleration can be expressed as the second derivative of position with respect to time.

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This segment focuses on practical application through problem-solving involving derivatives to find velocity and acceleration based on position functions provided.

Problem-Solving with Derivatives

• Calculating velocity involves deriving the given position function with respect to time.

• Deriving simple polynomial functions for velocity and acceleration simplifies problem-solving.

• Deriving the obtained velocity function yields the acceleration function.

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Exploring equations for motion in one dimension, specifically uniform linear motion (MR) and uniformly accelerated linear motion (M), highlighting differences in velocities and positions based on acceleration presence.

Equations for Linear Motion

• In uniform linear motion (MR), where there is no acceleration, position equals initial position plus constant speed multiplied by time.

Understanding Motion Graphs

In this section, the importance of distinguishing between motion with and without acceleration is discussed. The focus is on analyzing graphs representing position, velocity, and acceleration over time.

Distinguishing Motion Types

• When there is no acceleration:

• Two important graphs: position-time and velocity-time.

• Position depends linearly on time, resulting in a straight line graph.

• Understanding the position-time graph:

• Position varies linearly with time when there is no acceleration.

• Velocity remains constant (horizontal line) due to the absence of acceleration.

Accelerated Motion Analysis

• When there is acceleration:

• Three key graphs: position-time, velocity-time, and acceleration-time.

• Position varies with the square of time, leading to a curved graph (parabolic).

• Clarifying misconceptions:

• A curved graph does not imply curved motion; it represents position changes over time.

Graphical Representation Insights

• Analyzing velocity-time graph under acceleration:

• Velocity changes linearly with time based on the corresponding expression.

• Understanding acceleration representation:

• Acceleration depicted as a horizontal line due to its constant value over time.

Conclusion