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    es el movimiento de un cuerpo que sigue una trayectoria recta en la cual realiza desplazamientos iguales en intervalos de tiempo iguales.

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga es el movimiento de un cuerpo que sigue una trayectoria recta en la cual realiza desplazamientos iguales en intervalos de tiempo iguales. de este sitio.

    cuando un movil sigue una trayectoria recta en la cual realiza desplazamientos iguales en tiempos

    Encuentra una respuesta a tu pregunta cuando un movil sigue una trayectoria recta en la cual realiza desplazamientos iguales en tiempos iguales se dice que efec…

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    cuando un movil sigue una trayectoria recta en la cual realiza desplazamientos iguales en tiempos - Brainly.lat

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    Movimiento rectilíneo

    Movimiento rectilíneo

    Movimiento rectilíneo Cinemática

    Movimiento rectilíneo

    Movimiento rectilíneo

    Movimiento de caída de los cuerpos Regresión lineal

    Movimiento rectilíneo

    uniforme

    Movimiento rectilíneo

    u. acelerado

    Movimiento rectilíneo y uniforme

    Movimiento rectilíneo uniformemente acelerado

    Interpretación geométrica de la derivada

    Integral definida

    Movimiento rectilíneo

    Se denomina movimiento rectilíneo, aquél cuya trayectoria es una línea recta.

    En la recta situamos un origen O, donde estará un observador que medirá la posición del móvil en el instante . Las posiciones serán positivas si el móvil está a la derecha del origen y negativas si está a la izquierda del origen.

    Posición

    La posición del móvil se puede relacionar con el tiempo mediante una función .

    Desplazamiento

    Supongamos ahora que en el tiempo , el móvil se encuentra en posición , más tarde, en el instante el móvil se encontrará en la posición . Decimos que móvil se ha desplazado D en el intervalo de tiempo D, medido desde el instante al instante .

    Velocidad

    La velocidad media entre los instantes y está definida por

    Para determinar la velocidad en el instante , debemos hacer el intervalo de tiempo D tan pequeño como sea posible, en el límite cuando D tiende a cero.

    Pero dicho límite, es la definición de derivada de con respecto del tiempo .

    Para comprender mejor el concepto de velocidad media, resolvemos el siguiente ejercicio

    Ejercicio

    Una partícula se mueve a lo largo del eje X, de manera que su posición en cualquier instante está dada por =5·2+1, donde se expresa en metros y en segundos.

    Calcular su velocidad promedio en el intervalo de tiempo entre:

    2 y 3 s. 2 y 2.1 s. 2 y 2.01 s. 2 y 2.001 s. 2 y 2.0001 s.

    Calcula la velocidad en el instante =2 s.

    En el instante =2 s, =21 m

    ’ (s) ’ (m) Δ Δ m/s 3 46 25 1 25 2.1 23.05 2.05 0.1 20.5 2.01 21.2005 0.2005 0.01 20.05 2.001 21.020005 0.020005 0.001 20.005 2.0001 21.00200005 0.00200005 0.0001 20.0005

    ... ......... ...

    0 20

    Como podemos apreciar en la tabla, cuando el intervalo Δ0, la velocidad media tiende a 20 m/s. La velocidad en el instante =2 s es una velocidad media calculada en un intervalo de tiempo que tiende a cero.

    Calculamos la velocidad en cualquier instante

    La posición del móvil en el instante es =52+1

    La posición del móvil en el instante +Des  =5(+D)2+1=52+10D+5D2+1

    El desplazamiento es D==10D+5D2

    La velocidad media <> es

    La velocidad en el instante es el límite de la velocidad media cuando el intervalo de tiempo tiende a cero

    La velocidad en un instante se puede calcular directamente, hallando la derivada de la posición respecto del tiempo.

    En el instante=2 s, =20 m/s

    Aceleración

    En general, la velocidad de un cuerpo es una función del tiempo. Supongamos que en un instante la velocidad del móvil es , y en el instante la velocidad del móvil es . Se denomina aceleración media entre los instantes y al cociente entre el cambio de velocidad D y el intervalo de tiempo en el que se ha tardado en efectuar dicho cambio, D.

    La aceleración en el instante es el límite de la aceleración media cuando el intervalo D tiende a cero, que es la definición de la derivada de v.

    Ejemplo:

    Un cuerpo se mueve a lo largo de una línea recta =23-42+5 m. Hallar la expresión de

    La velocidad

    La aceleración del móvil en función del tiempo.

    Dada la velocidad del móvil hallar el desplazamiento

    Si conocemos un registro de la velocidad podemos calcular el desplazamiento del móvil entre los instantes y , mediante la integral definida.

    El producto representa el desplazamiento del móvil entre los instantes y , o en el intervalo . El desplazamiento total es la suma de los infinitos desplazamientos infinitesimales entre los instantes y .

    En la figura, se muestra una gráfica de la velocidad en función del tiempo, el área en color azul mide el desplazamiento total del móvil entre los instantes y , el segmento en color azul marcado en la trayectoria recta.

    Hallamos la posición del móvil en el instante , sumando la posición inicial al desplazamiento, calculado mediante la medida del área bajo la curva v-t o mediante cálculo de la integral definida en la fórmula anterior.

    Ejemplo:

    Un cuerpo se mueve a lo largo de una línea recta de acuerdo a la ley 45 m/s. Si en el instante =2 s. está situado en =4 m del origen. Calcular la posición del móvil en cualquier instante.

    Dada la aceleración del móvil hallar el cambio de velocidad

    Del mismo modo, que hemos calculado el desplazamiento del móvil entre los instantes y , a partir de un registro de la velocidad en función del tiempo , podemos calcular el cambio de velocidad que experimenta el móvil entre dichos instantes, a partir de un registro de la aceleración en función del tiempo.

    fuente : www.sc.ehu.es

    Movimiento Rectilíneo Uniforme (artículo)

    Movimiento rectilíneo uniforme (MRU)

    Movimiento Rectilíneo Uniforme

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    Correo electrónico

    Movimiento rectilíneo uniforme (MRU)

    Imagina que eres un astronauta en la Estación Espacial Internacional. Estás arreglando unos paneles solares averiados, cuando de pronto, al presionar, tu destornillador sale disparado de tus manos. Si no lo atrapas a tiempo, el destornillador estará viajando por el espacio en línea recta y a velocidad constante, a menos que algo se interponga en su camino. Esto sucede porque la herramienta se mueve con movimiento rectilíneo uniforme, o MRU.

    Foto de la Estación Espacial Internacional

    Estación Epacial Internacional orbitando nuestro planeta. Créditos: International Space Station orbiting above earth de la National Reconnaissance Office.

    El MRU se define el movimiento en el cual un objeto se desplaza en línea recta, en una sola dirección, recorriendo distancias iguales en el mismo intervalo de tiempo, manteniendo en todo su movimiento una velocidad constante y sin aceleración.

    Recuerda que la velocidad es un vector, entonces, al ser constante, no varía ni su magnitud, ni su dirección de movimiento.

    Condiciones del MRU

    Para que un cuerpo esté en MRU, es necesario que se cumpla la siguiente relación:

    \Large (v= \dfrac{x-x_0}{t-t_0}) =

    (v= t−t 0 ​ x−x 0 ​ ​ )=

    left parenthesis, v, equals, start fraction, x, minus, x, start subscript, 0, end subscript, divided by, t, minus, t, start subscript, 0, end subscript, end fraction, right parenthesis, equals

    Constante Donde \Large x x x

    : es la posición en el espacio y

    \Large t t t : es el tiempo.

    De esta condición, llegamos a la ecuación del MRU:

    \Large x = x_0 + v(t-t_0)

    x=x 0 ​ +v(t−t 0 ​ )

    x, equals, x, start subscript, 0, end subscript, plus, v, left parenthesis, t, minus, t, start subscript, 0, end subscript, right parenthesis

    Donde: \Large x_0 x 0 ​

    x, start subscript, 0, end subscript

    : posición en el instante

    \Large t_0 t 0 ​

    t, start subscript, 0, end subscript

    \Large x x x

    : Posición en el instante

    \Large t t t

    Esto quiere decir que si conocemos la posición

    x_0 x 0 ​

    x, start subscript, 0, end subscript

    en el instante t_0 t 0 ​

    t, start subscript, 0, end subscript

    y sabemos cuál es la de la velocidad

    v v v

    , podremos conocer la posición

    x x x

    en cualquier instante

    t t t .

    ¡No olvides fijarte bien en las unidades que utilizas y de convertirlas si es necesario!

    Veamos un ejemplo:

    Imagínate que has programado un carro robótico para que tenga una velocidad constante de

    10\text{ m/s} 10 m/s

    10, start text, space, m, slash, s, end text

    . ¿Puedes calcular a qué distancia desde el punto de partida estará luego de

    30\text{ s} 30 s

    30, start text, space, s, end text

    ?

    Tienes los siguientes datos:

    \begin{aligned}v&= 10 \text{ m/s}\\\\ x_0&=0\text{ m}\\\\ t_0&=0\text{ s}\\\\ t&=30\text{ s}\end{aligned}

    v x 0 ​ t 0 ​ t ​ =10 m/s =0 m =0 s =30 s ​

    Aplicando la fórmula de MRU:

    \begin{aligned}x&= 0 \text{ m} + 10 \text{ m/s}(30\text{ s}-0\text{ s})\\\\ x &= 0\text{ m}+ 300 \text{ m}\\\\ x&= 300 \text{ m}\end{aligned}

    x x x ​

    =0 m+10 m/s(30 s−0 s)

    =0 m+300 m =300 m ​ A los 30 30 30

    segundos, tu carro se habrá desplazado

    300 300 300 metros.

    Veamos más ejemplos

    Puedes ver que si el instante y la posición iniciales se asumen como

    0 0 0

    , la ecuación queda simplificada:

    \Large x= vt x=vt x, equals, v, t

    Ahora, si sabes que una canica se mueve con MRU, y has medido que en

    20 20 20 segundos, recorre 40 40 40

    metros, ¿podrías hallar su velocidad? ¡Inténtalo!

    [Muéstrame el procedimiento]

    Veamos otro ejemplo: Si te desplazas con MRU en tu scooter a 10

    \text{ m/s} m/s

    start text, space, m, slash, s, end text

    y quieres llegar al parque que está en línea recta a una distancia de 450 metros, ¿en cuánto tiempo llegarías?

    ¿Puedes resolverlo?

    [Muéstrame el procedimiento]

    Compliquemos un poco las cosas.

    Imagínate que un bus de pasajeros va en MRU a

    60 \text{ km/h} 60 km/h

    60, start text, space, k, m, slash, h, end text

    . Dos horas más tarde, parte un auto particular desde el mismo punto, con una velocidad de

    80 \text{ km/h} 80 km/h

    80, start text, space, k, m, slash, h, end text

    .

    a) ¿Cuántos kilómetros ha recorrido el bus de pasajeros al momento de partida del auto?

    b) ¿A qué distancia del punto de partida se encuentran ambos vehículos?

    Resolvamos esto juntos:

    fuente : es.khanacademy.org

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    Santiago 10 day ago
    4

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