Questions: Tracez approximativement le graphe de la position en fonction du temps d'un objet (a) immobile à x=3 m; (b) partant de l'origine avec une vitesse constante vx>0; (c) partant de x<0 avec une vitesse vx>0 et une accélération ax>0.

Tracez approximativement le graphe de la position en fonction du temps d'un objet (a) immobile à x=3 m; (b) partant de l'origine avec une vitesse constante vx>0; (c) partant de x<0 avec une vitesse vx>0 et une accélération ax>0.

Transcript text: R1. Tracez approximativement le graphe de la position en fonction du temps d'un objet (a) immobile à $x=3 \mathrm{~m}$; (b) partant de l'origine avec une vitesse constante $v_{x}>0$; (c) partant de $x<0$ avec une vitesse $v_{x}>0$ et une accélération $a_{x}>0$.

Solution

Solution Steps

Step 1: Understanding the Problem

We need to sketch the position vs. time graphs for three different scenarios involving an object's motion. Each scenario describes a different type of motion.

Step 2: Scenario (a) - Object at Rest

For an object that is immobile at $ x = 3 \, \text{m} $, the position does not change over time. The graph will be a horizontal line at $ x = 3 \, \text{m} $.

Step 3: Scenario (b) - Constant Positive Velocity

For an object starting from the origin with a constant positive velocity $ v_x > 0 $, the position increases linearly over time. The graph will be a straight line passing through the origin with a positive slope.

Step 4: Scenario (c) - Positive Velocity and Acceleration

For an object starting from $ x < 0 $ with a positive velocity $ v_x > 0 $ and a positive acceleration $ a_x > 0 $, the position increases non-linearly over time. The graph will be a curve starting from a negative position and curving upwards, indicating increasing velocity.

Final Answer

(a) The graph for an immobile object at $ x = 3 \, \text{m} $: \[ \boxed{\text{Horizontal line at } x = 3 \, \text{m}} \]

(b) The graph for an object starting from the origin with a constant positive velocity $ v_x > 0 $: \[ \boxed{\text{Straight line with positive slope passing through the origin}} \]

(c) The graph for an object starting from $ x < 0 $ with a positive velocity $ v_x > 0 $ and a positive acceleration $ a_x > 0 $: \[ \boxed{\text{Upward curving line starting from a negative position}} \]

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