Ecrit par ✅ Quiz : Relativite De La Simultaneite
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": "Relativite De La Simultaneite",
"quiz_slug": "04_relativite_de_la_simultaneite_quiz",
"quiz_description": "Quiz Edu509 : Relativite De La Simultaneite",
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"time_type": "minutes"
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"questions": [
{
"question_order": 1,
"question_title": "Deux événements ont lieu aux positions \\\\( x_1 = 0 \\\\mathrm{m} \\\\) et \\\\( x_2 = 300 \\\\mathrm{m} \\\\) dans le référentiel S, au même instant \\\\( t_1 = t_2 = 0 \\\\mathrm{s} \\\\). Le train (S’) se déplace à \\\\( v = 0{,}6c \\\\) par rapport au quai. Quelles affirmations sont correctes dans le référentiel du train ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans le référentiel du train, \\\\( t_1' = 0 \\\\mathrm{s} \\\\) et \\\\( t_2' = -7{,}5 \\\\times 10^{-7} \\\\mathrm{s} \\\\). L’événement à \\\\( x_2 \\\\) a donc lieu avant celui à \\\\( x_1 \\\\), et ils ne sont pas simultanés.",
"answers": [
{
"answer_title": "Les deux événements ne sont pas simultanés dans le train.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "L’événement à \\\\( x_2 \\\\) a lieu avant celui à \\\\( x_1 \\\\) dans le train.",
"is_correct": true,
"answer_order": 2
},
{
"answer_title": "Les deux événements sont simultanés dans le train.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "L’événement à \\\\( x_1 \\\\) a lieu avant celui à \\\\( x_2 \\\\) dans le train.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Dans la transformation de Lorentz pour le temps, quelle est l’expression correcte du facteur \\\\( \\\\gamma \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le facteur de Lorentz est défini par \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - \\\\frac{v^2}{c^2}}} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - \\\\frac{v^2}{c^2}}} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\gamma = \\\\sqrt{1 - \\\\frac{v^2}{c^2}} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\gamma = 1 - \\\\frac{v^2}{c^2} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\gamma = \\\\frac{v}{c} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Deux lampes s’allument simultanément à \\\\( t_1 = t_2 = 2{,}0 \\\\mathrm{s} \\\\) dans S, à \\\\( x_1 = -150 \\\\mathrm{m} \\\\) et \\\\( x_2 = +150 \\\\mathrm{m} \\\\). Un observateur se déplace à \\\\( v = 0{,}8c \\\\) vers \\\\( x_2 \\\\). Quelle est la différence de temps entre les deux allumages dans le référentiel de l’observateur ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le calcul donne \\\\( t_1' \\\\approx 3{,}34 \\\\mathrm{s} \\\\) et \\\\( t_2' \\\\approx 3{,}33 \\\\mathrm{s} \\\\), donc \\\\( \\\\Delta t' = -0{,}01 \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t' = -0{,}01 \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t' = 0 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t' = +0{,}01 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t' = -1{,}0 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Un train de \\\\( 600 \\\\mathrm{m} \\\\) de long se déplace à \\\\( v = 0{,}5c \\\\). Deux pétards explosent simultanément aux extrémités du train dans S. Selon un observateur au centre du train, lequel explose en premier ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans le référentiel du train, \\\\( t_2' = -1{,}155 \\\\times 10^{-6} \\\\mathrm{s} \\\\) (avant) et \\\\( t_1' = 0 \\\\mathrm{s} \\\\) (arrière), donc l’avant explose en premier.",
"answers": [
{
"answer_title": "Le pétard à l’avant explose en premier.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Le pétard à l’arrière explose en premier.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Les deux pétards explosent en même temps.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Impossible de déterminer sans plus d’informations.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Quelle affirmation est vraie concernant la simultanéité 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 simultanéité n’est pas absolue, mais relative au référentiel de l’observateur.",
"answers": [
{
"answer_title": "La simultanéité dépend du référentiel de l’observateur.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La simultanéité est absolue pour tous les observateurs.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La simultanéité dépend uniquement de la distance entre les événements.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "La simultanéité n’existe pas en physique moderne.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Deux horloges sont placées à \\\\( x_1 = 0 \\\\mathrm{m} \\\\) et \\\\( x_2 = 400 \\\\mathrm{m} \\\\) sur un quai. Un train passe à \\\\( v = 0{,}4c \\\\). Pour un passager du train, quelle est la différence de temps entre les deux sonneries ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le calcul donne \\\\( t_1' = 0 \\\\mathrm{s} \\\\) et \\\\( t_2' = -5{,}81 \\\\times 10^{-7} \\\\mathrm{s} \\\\), donc \\\\( \\\\Delta t' = -5{,}81 \\\\times 10^{-7} \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t' = -5{,}81 \\\\times 10^{-7} \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t' = 0 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t' = +5{,}81 \\\\times 10^{-7} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t' = -4{,}00 \\\\times 10^{-7} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Dans la transformation de Lorentz, que représente la variable \\\\( x \\\\) dans la formule \\\\( t' = \\\\gamma ( t - \\\\frac{v x}{c^2} ) \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans la formule, \\\\( x \\\\) est la position de l’événement dans le référentiel S.",
"answers": [
{
"answer_title": "La position de l’événement dans le référentiel S.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "La position de l’événement dans le référentiel S’.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "La vitesse de l’observateur.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Le temps de l’événement dans S.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Deux feux d’artifice explosent simultanément à \\\\( x_1 = -200 \\\\mathrm{m} \\\\) et \\\\( x_2 = +200 \\\\mathrm{m} \\\\) sur un quai. Un train passe à \\\\( v = 0{,}7c \\\\). Quelle est la différence de temps entre les deux explosions selon un passager du train ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le calcul donne \\\\( \\\\Delta t' = -1{,}31 \\\\times 10^{-6} \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t' = -1{,}31 \\\\times 10^{-6} \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t' = 0 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t' = +1{,}31 \\\\times 10^{-6} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t' = -2{,}10 \\\\times 10^{-6} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Dans l’expérience du train et du quai, pourquoi la lumière de l’éclair à l’avant du train atteint-elle le passager avant celle de l’arrière selon le passager ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le train avance vers l’avant, donc le passager se rapproche de la lumière venant de l’avant et s’éloigne de celle venant de l’arrière. De plus, la simultanéité dépend du référentiel.",
"answers": [
{
"answer_title": "Parce que le train avance vers l’avant et s’éloigne de l’arrière.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Parce que la lumière va plus vite vers l’avant.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Parce que la vitesse de la lumière dépend du référentiel.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Parce que les deux éclairs ne sont pas simultanés dans tous les référentiels.",
"is_correct": true,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Quelle est la valeur de \\\\( \\\\gamma \\\\) pour \\\\( v = 0{,}8c \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour \\\\( v = 0{,}8c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - 0{,}64}} = \\\\frac{1}{0{,}6} = 1{,}67 \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}67 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}25 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}40 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 2{,}00 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Si deux événements sont simultanés dans S mais ont des positions différentes, que peut-on affirmer dans S’ en mouvement par rapport à S ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La transformation de Lorentz montre que la simultanéité dépend du référentiel si les positions sont différentes.",
"answers": [
{
"answer_title": "Ils ne sont généralement pas simultanés dans S’.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Ils sont toujours simultanés dans S’.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Ils ont toujours lieu au même endroit dans S’.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Ils sont séparés par un intervalle de temps nul dans S’.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Dans la transformation de Lorentz, si \\\\( v = 0 \\\\), que vaut \\\\( t' \\\\) ?",
"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 \\\\( \\\\gamma = 1 \\\\) et \\\\( t' = t \\\\).",
"answers": [
{
"answer_title": "\\\\( t' = t \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( t' = 0 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( t' = \\\\gamma t \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( t' = \\\\frac{t}{\\\\gamma} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Un observateur mesure deux événements à \\\\( x_1 = 0 \\\\mathrm{m} \\\\), \\\\( t_1 = 0 \\\\mathrm{s} \\\\) et \\\\( x_2 = 600 \\\\mathrm{m} \\\\), \\\\( t_2 = 0 \\\\mathrm{s} \\\\) dans S. Le train va à \\\\( v = 0{,}5c \\\\). Quelle est la différence de temps entre les deux événements dans le train ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le calcul donne \\\\( \\\\Delta t' = -1{,}155 \\\\times 10^{-6} \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "\\\\( -1{,}155 \\\\times 10^{-6} \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 0 \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( +1{,}155 \\\\times 10^{-6} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( -6{,}00 \\\\times 10^{-7} \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Quelle est la valeur de \\\\( \\\\gamma \\\\) pour \\\\( v = 0{,}7c \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour \\\\( v = 0{,}7c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - 0{,}49}} = \\\\frac{1}{\\\\sqrt{0{,}51}} \\\\approx 1{,}40 \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}40 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}25 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}67 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}09 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Dans la transformation de Lorentz, si \\\\( x = 0 \\\\), que vaut \\\\( t' \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Si \\\\( x = 0 \\\\), alors \\\\( t' = \\\\gamma t \\\\).",
"answers": [
{
"answer_title": "\\\\( t' = \\\\gamma t \\\\)",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "\\\\( t' = t \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( t' = 0 \\\\)",
"is_correct": true,
"answer_order": 3
},
{
"answer_title": "\\\\( t' = \\\\frac{t}{\\\\gamma} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Pour \\\\( v = 0{,}4c \\\\), quelle est la valeur de \\\\( \\\\gamma \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour \\\\( v = 0{,}4c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - 0{,}16}} = \\\\frac{1}{\\\\sqrt{0{,}84}} \\\\approx 1{,}09 \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}09 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}25 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}40 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}67 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Dans la transformation de Lorentz, que signifie le terme \\\\( -\\\\frac{v x}{c^2} \\\\) dans \\\\( t' = \\\\gamma ( t - \\\\frac{v x}{c^2} ) \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le terme \\\\( -\\\\frac{v x}{c^2} \\\\) traduit le décalage temporel dû au mouvement relatif entre référentiels.",
"answers": [
{
"answer_title": "Il traduit le décalage temporel dû au déplacement de l’observateur.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Il exprime la contraction des longueurs.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Il donne la vitesse de la lumière.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Il correspond à la dilatation du temps.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Deux événements ont lieu à \\\\( x_1 = 0 \\\\mathrm{m} \\\\), \\\\( t_1 = 0 \\\\mathrm{s} \\\\) et \\\\( x_2 = 400 \\\\mathrm{m} \\\\), \\\\( t_2 = 0 \\\\mathrm{s} \\\\) dans S. Le train va à \\\\( v = 0{,}4c \\\\). Selon le passager du train, lequel des deux événements a lieu en premier ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Dans le train, \\\\( t_2' = -5{,}81 \\\\times 10^{-7} \\\\mathrm{s} \\\\) et \\\\( t_1' = 0 \\\\mathrm{s} \\\\), donc \\\\( x_2 \\\\) a lieu en premier.",
"answers": [
{
"answer_title": "L’événement à \\\\( x_2 \\\\) a lieu en premier.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "L’événement à \\\\( x_1 \\\\) a lieu en premier.",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "Les deux événements sont simultanés.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Impossible de savoir.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Pour \\\\( v = 0{,}6c \\\\), quelle est la valeur de \\\\( \\\\gamma \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour \\\\( v = 0{,}6c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - 0{,}36}} = \\\\frac{1}{0{,}8} = 1{,}25 \\\\).",
"answers": [
{
"answer_title": "\\\\( 1{,}25 \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( 1{,}67 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( 1{,}40 \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( 1{,}09 \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Si deux événements sont simultanés dans S et ont \\\\( x_1 = -a \\\\), \\\\( x_2 = +a \\\\), alors dans S’ en mouvement à vitesse \\\\( v \\\\), la différence de temps entre les deux événements est :",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On a \\\\( t_1' = \\\\gamma (0 - \\\\frac{v (-a)}{c^2}) = \\\\gamma \\\\frac{v a}{c^2} \\\\) et \\\\( t_2' = \\\\gamma (0 - \\\\frac{v a}{c^2}) = -\\\\gamma \\\\frac{v a}{c^2} \\\\), donc \\\\( \\\\Delta t' = t_2' - t_1' = -2 \\\\gamma \\\\frac{v a}{c^2} \\\\).",
"answers": [
{
"answer_title": "\\\\( \\\\Delta t' = -2 \\\\gamma \\\\frac{v a}{c^2} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( \\\\Delta t' = 0 \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( \\\\Delta t' = 2 \\\\gamma \\\\frac{v a}{c^2} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( \\\\Delta t' = \\\\gamma \\\\frac{v a}{c^2} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
}
]
}