Import Question JSON

Current Question (ID: 8906)

Question:

$\text{The graph of displacement time is given below.}$ $\text{Its corresponding velocity-time graph will be:}$

Options:

1. $\text{Velocity-time graph showing a straight line decreasing from positive to negative}$
2. $\text{Velocity-time graph showing a parabolic curve opening upward}$
3. $\text{Velocity-time graph showing a parabolic curve opening downward}$
4. $\text{Velocity-time graph showing a straight line increasing from negative to positive}$

Solution:

$\text{Hint: } v = \frac{ds}{dt}$ $\text{Step: Identify the graph for the } v-t.$ $\text{The displacement vs time (s vs. t) graph is a parabola.}$ $\text{Let the equation of the parabola is } s = kt^2$ $\text{The velocity of the particle is given by;}$ $v = \frac{ds}{dt} = 2kt$ $\text{So } v \text{ vs. } t \text{ must be line and at } t = 0, \frac{ds}{dt} > 0 \text{ - as shown in the graph below;}$ $\text{Hence, option (1) is the correct answer.}$

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
}