Import Question JSON

Current Question (ID: 9853)

Question:

$\text{The energy required to accelerate a car from rest to 30 m/s is E. The energy required to accelerate the car from 30 m/s to 60 m/s will be:}$

Options:

1. $E$
2. $2E$
3. $3E$
4. $4E$

Solution:

\text{Using the kinetic energy formula } KE = \frac{1}{2}mv^2 \text{Energy to accelerate from 0 to 30 m/s:} E = \frac{1}{2}m(30)^2 = \frac{1}{2}m(900) = 450m \text{Energy to accelerate from 30 m/s to 60 m/s is the difference in kinetic energies:} \text{Energy} = \frac{1}{2}m(60)^2 - \frac{1}{2}m(30)^2 = \frac{1}{2}m(3600) - \frac{1}{2}m(900) = 1800m - 450m = 1350m \text{Since } E = 450m\text{, then } 1350m = 3E \text{Therefore, the energy required to accelerate from 30 m/s to 60 m/s is } 3E

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}