Import Question JSON

Current Question (ID: 8890)

Question:

$\text{For the given acceleration }(a)\text{ versus time }(t)\text{ graph of a body, the body is initially at rest.}$ $\text{The acceleration-time graph shows acceleration starting at a positive value and decreasing linearly to zero.}$ $\text{From the following, the velocity }(v)\text{ versus time }(t)\text{ graph will be:}$

Options:

1. $\text{Graph 1: Linear increasing line starting from origin with constant positive slope}$
2. $\text{Graph 2: Linear decreasing line starting from a positive value}$
3. $\text{Graph 3: Curved line starting from origin, increasing with decreasing slope (concave downward)}$
4. $\text{Graph 4: Curved line starting from origin, increasing with increasing slope (concave upward)}$

Solution:

$\text{Hint: The acceleration is positive and decreasing at a constant rate.}$ $\text{Step 1: Identify the change in acceleration from a-t graph.}$ $\text{From the a-t graph, we observed that a is +ve and decreasing.}$ $\text{Step 2: Find the required slope for velocity-time graph.}$ $\text{Since } a = \frac{dv}{dt}\text{, the acceleration represents the slope of the velocity-time graph.}$ $\text{The slope of the velocity-time graph is positive and with a decreasing angle with the +ve x-axis.}$ $\text{This means:}$ $\text{- Velocity starts at zero (body initially at rest)}$ $\text{- Velocity increases (positive acceleration)}$ $\text{- Rate of increase decreases (decreasing acceleration)}$ $\text{- This creates a concave downward curve}$ $\text{Therefore, option (3) is the correct velocity }(v)\text{ versus time }(t)\text{ graph.}$ $\text{Hence, option (3) is the correct answer.}$

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
}