Import Question JSON

Current Question (ID: 19113)

Question:

$\text{The displacement of a particle changes with time as}$ $x = 6t^3 - 12t^2 + 20t + 30.$ $\text{The velocity of the particle when its acceleration becomes zero (} t \text{ is time in s) is:}$

Options:

1. $12 \text{ m/s}$
2. $14 \text{ m/s}$
3. $18 \text{ m/s}$
4. $20 \text{ m/s}$

Solution:

$\text{Hint: } v = \frac{dx}{dt}$ $v = \frac{dx}{dt} = 20$ $= 18t^2 - 24t + 20$ $a = \frac{dv}{dt} = 36t - 24$ $\text{At } a = 0$ $t = \frac{24}{36} = \frac{2}{3} \text{ sec}$ $\text{Then, } v = 18 \times \frac{4}{9} - 24 \times \frac{2}{3} + 20$ $= 8 - 16 + 20 = 12 \text{ m/s}$

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
}