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Current Question (ID: 9559)

Question:

$\text{A particle is moving such that its position coordinates } (x, y) \text{ are } (2 \text{ m}, 3 \text{ m}) \text{ at time } t = 0, (6 \text{ m}, 7 \text{ m}) \text{ at time } t = 2 \text{ s and } (13 \text{ m}, 14 \text{ m}) \text{ at time } t = 5 \text{ s. The average velocity vector } (v_{avg}) \text{ from } t = 0 \text{ to } t = 5 \text{ s is:}$

Options:

1. $\frac{1}{5}(13\hat{i} + 14\hat{j})$
2. $\frac{7}{3}(\hat{i} + \hat{j})$
3. $2(\hat{i} + \hat{j})$
4. $\frac{11}{5}(\hat{i} + \hat{j})$

Solution:

\text{Hint: } \vec{v}_{AB} = \frac{\text{net displacement}}{\text{time taken}} \text{Step: Find the average velocity vector of the particle.} \vec{v}_{AB} = \frac{\text{net displacement}}{\text{time taken}} \vec{v}_{AB} = \frac{(13-2)\hat{i} + (14-3)\hat{j}}{5} \vec{v}_{AB} = \frac{(11)\hat{i} + (11)\hat{j}}{5} \vec{v}_{AB} = \frac{11}{5}(\hat{i} + \hat{j}) \text{Therefore, the average velocity vector of the particle is } \frac{11}{5}(\hat{i} + \hat{j}). \text{Hence, option (4) is the correct answer.}

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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
}