Ecrit par ✅ Quiz : Dilation Du Temps
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
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{
"quiz_title": "Dilation Du Temps",
"quiz_slug": "05_dilation_du_temps_quiz",
"quiz_description": "Quiz Edu509 : Dilation Du Temps",
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"questions": [
{
"question_order": 1,
"question_title": "Quelle est la formule correcte de la dilation du temps selon la relativité restreinte ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La formule correcte de la dilation du temps est \\\\( \\\\Delta t = \\\\frac{\\\\Delta t_0}{\\\\sqrt{1 - \\\\frac{v^2}{c^2}}} \\\\), comme démontré dans la leçon.",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t = \\\\frac{\\\\Delta t_0}{\\\\sqrt{1 - \\\\frac{v^2}{c^2}}} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t = \\\\Delta t_0 \\\\sqrt{1 - \\\\frac{v^2}{c^2}} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t = \\\\Delta t_0 (1 - \\\\frac{v^2}{c^2}) \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t = \\\\frac{\\\\Delta t_0}{1 - \\\\frac{v^2}{c^2}} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un processus dure \\\\( 5,0 \\\\mathrm{s} \\\\) dans le référentiel propre d’un vaisseau voyageant à \\\\( 0,80c \\\\). Quelle durée mesure un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\( \\\\Delta t = \\\\frac{5,0}{\\\\sqrt{1 - (0,80)^2}} = \\\\frac{5,0}{0,60} = 8,3 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "8,3 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "5,0 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "3,0 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "10,0 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Si la vitesse relative \\\\( v \\\\) entre deux référentiels augmente et approche \\\\( c \\\\), que se passe-t-il pour \\\\( \\\\Delta t \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Lorsque \\\\( v \\\\) approche \\\\( c \\\\), le dénominateur diminue et \\\\( \\\\Delta t \\\\) augmente fortement.",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t \\\\) augmente",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t \\\\) diminue",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t \\\\) reste constant",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t \\\\) devient négatif",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Un muon a une durée de vie propre de \\\\( 2,2 \\\\mathrm{\\\\mu s} \\\\) et se déplace à \\\\( 0,98c \\\\). Quelle est sa durée de vie mesurée sur Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\( \\\\Delta t = \\\\frac{2,2}{\\\\sqrt{1 - (0,98)^2}} \\\\approx \\\\frac{2,2}{0,199} \\\\approx 11,1 \\\\mathrm{\\\\mu s} \\\\).",
"answers": [
{
"answer_title": "11,1 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,2 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "4,4 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,98 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Pour un vaisseau allant à \\\\( 0,60c \\\\), un intervalle de temps propre de \\\\( 2,0 \\\\mathrm{s} \\\\) correspond à combien de temps mesuré sur Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Avec \\\\( v = 0,60c \\\\), \\\\( \\\\Delta t = \\\\frac{2,0}{0,80} = 2,5 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "2,5 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,0 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,6 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,3 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Quelle affirmation est correcte concernant le temps propre \\\\( \\\\Delta t_0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps propre est mesuré dans le référentiel où l’événement se produit au même endroit.",
"answers": [
{
"answer_title": "Il est mesuré dans le référentiel où l’événement se produit au même endroit.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Il est toujours plus grand que le temps dilaté.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Il dépend de la vitesse de l’observateur.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Il est mesuré par l’observateur en mouvement.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Un vaisseau parcourt 8,6 années-lumière à \\\\( 0,95c \\\\). Quelle durée de voyage mesure l’équipage ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps propre est \\\\( \\\\Delta t_0 = 9,05 \\\\times 0,312 = 2,8 \\\\) ans.",
"answers": [
{
"answer_title": "2,8 ans",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "8,6 ans",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "9,1 ans",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,95 ans",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Pour une particule à \\\\( 0,70c \\\\) ayant une durée de vie propre de \\\\( 10,0 \\\\mathrm{\\\\mu s} \\\\), quelle est sa durée de vie mesurée par un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\( \\\\Delta t = \\\\frac{10,0}{0,714} = 14,0 \\\\mathrm{\\\\mu s} \\\\).",
"answers": [
{
"answer_title": "14,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "10,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "7,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "17,1 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Si \\\\( v = 0 \\\\), que vaut \\\\( \\\\Delta t \\\\) par rapport à \\\\( \\\\Delta t_0 \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\( v = 0 \\\\), alors \\\\( \\\\sqrt{1 - 0} = 1 \\\\), donc \\\\( \\\\Delta t = \\\\Delta t_0 \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t = \\\\Delta t_0 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t > \\\\Delta t_0 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t < \\\\Delta t_0 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t = 0 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Quel est le rôle de la vitesse de la lumière \\\\( c \\\\) dans la formule de la dilation du temps ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La vitesse de la lumière \\\\( c \\\\) est la vitesse limite dans la relativité restreinte.",
"answers": [
{
"answer_title": "C’est la vitesse limite qui ne peut pas être dépassée.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "C’est la vitesse minimale possible.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Elle n’a aucun effet sur la formule.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Elle est utilisée seulement pour les ondes.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Un événement dure \\\\( 1,5 \\\\mathrm{\\\\mu s} \\\\) dans le référentiel propre d’une particule à \\\\( 0,80c \\\\). Quelle durée mesure un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\( \\\\Delta t = \\\\frac{1,5}{0,60} = 2,5 \\\\mathrm{\\\\mu s} \\\\).",
"answers": [
{
"answer_title": "2,5 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,5 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "1,2 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Dans la formule \\\\( \\\\Delta t = \\\\frac{\\\\Delta t_0}{\\\\sqrt{1 - \\\\frac{v^2}{c^2}}} \\\\), que se passe-t-il si \\\\( v \\\\) devient égal à \\\\( c \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\( v = c \\\\), le dénominateur devient zéro, donc \\\\( \\\\Delta t \\\\) tend vers l’infini.",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t \\\\) tend vers l’infini",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t = 0 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t = \\\\Delta t_0 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t \\\\) devient négatif",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Quel est le temps mesuré sur Terre pour un voyage de 12 années-lumière à \\\\( 0,80c \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Temps dans le référentiel terrestre : \\\\( \\\\Delta t = \\\\frac{12}{0,80} = 15,0 \\\\) ans.",
"answers": [
{
"answer_title": "15,0 ans",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "12,0 ans",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "9,6 ans",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "7,2 ans",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Pour une vitesse \\\\( v = 0,99c \\\\), quel est le facteur de dilation du temps \\\\( \\\\gamma \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le facteur \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - (0,99)^2}} = \\\\frac{1}{\\\\sqrt{0,0199}} \\\\approx 7,09 \\\\).",
"answers": [
{
"answer_title": "7,09",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,41",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,99",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,14",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Un processus dure \\\\( 20,0 \\\\mathrm{s} \\\\) dans le référentiel propre d’un vaisseau à \\\\( 0,90c \\\\). Quelle durée mesure un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule : \\\\( \\\\sqrt{1 - 0,81} = 0,4359 \\\\), donc \\\\( \\\\Delta t = \\\\frac{20,0}{0,4359} \\\\approx 45,8 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "45,8 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "20,0 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "18,0 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "28,6 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Pour une particule à \\\\( 0,50c \\\\) ayant une durée de vie propre de \\\\( 4,0 \\\\mathrm{\\\\mu s} \\\\), quelle est sa durée de vie mesurée par un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\( \\\\sqrt{1 - 0,25} = 0,866 \\\\), donc \\\\( \\\\Delta t = \\\\frac{4,0}{0,866} \\\\approx 4,6 \\\\mathrm{\\\\mu s} \\\\).",
"answers": [
{
"answer_title": "4,6 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "8,0 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,5 \\\\( \\\\mathrm{\\\\mu s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Si un observateur mesure un temps plus long que le temps propre, que peut-on dire de sa vitesse relative ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Un temps dilaté implique une vitesse relative non nulle, proche de \\\\( c \\\\).",
"answers": [
{
"answer_title": "Elle est non nulle et proche de \\\\( c \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Elle est nulle",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Elle est infinie",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Elle est négative",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Pour \\\\( v \\\\ll c \\\\), que devient la formule de la dilation du temps ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour \\\\( v \\\\ll c \\\\), \\\\( \\\\frac{v^2}{c^2} \\\\) est négligeable, donc \\\\( \\\\Delta t \\\\approx \\\\Delta t_0 \\\\).",
"answers": [
{
"answer_title": "Le temps dilaté est pratiquement égal au temps propre",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Le temps dilaté est beaucoup plus grand",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Le temps dilaté est négatif",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Le temps dilaté est nul",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Un vaisseau se déplace à \\\\( 0,99c \\\\). Un processus dure \\\\( 1,0 \\\\mathrm{s} \\\\) dans le référentiel du vaisseau. Quelle durée mesure un observateur terrestre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le facteur de dilation est \\\\( 7,09 \\\\), donc \\\\( \\\\Delta t = 1,0 \\\\times 7,09 = 7,09 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "7,09 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,0 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,99 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "14,1 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Quelle(s) grandeur(s) doit/doivent être dans la même unité pour utiliser la formule de la dilation du temps ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Il faut que \\\\( v \\\\) et \\\\( c \\\\) soient dans la même unité pour appliquer la formule correctement.",
"answers": [
{
"answer_title": "La vitesse \\\\( v \\\\) et la vitesse de la lumière \\\\( c \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Le temps propre et la distance",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La masse et la vitesse",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La distance et la vitesse de la lumière",
"is_correct": false,
"answer_order": 4
}
]
}
]
}