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Current Question (ID: 9594)

Question:

$\text{A particle has an initial velocity } \vec{u} = (4\hat{i} - 5\hat{j}) \text{ m/s and it is moving with an acceleration } \vec{a} = \left(\frac{1}{4}\hat{i} + \frac{3}{5}\hat{j}\right) \text{ m/s}^2. \text{ Velocity of the particle at } t = 2 \text{ s will be:}$

Options:

1. $(6\hat{i} - 4\hat{j}) \text{ m/s}$
2. $(4.5\hat{i} - 4.5\hat{j}) \text{ m/s}$
3. $(4.5\hat{i} - 4.6\hat{j}) \text{ m/s}$
4. $(6\hat{i} - 4.6\hat{j}) \text{ m/s}$

Solution:

\text{Hint: Use the first motion equation.} \text{Step: Find the velocity of the particle at t = 2 s.} \text{The velocity formula is: } v = u + at v = (4i - 5j) + (0.25i + 0.6j) \times 2 \text{Calculate acceleration term:} at = (0.25 \times 2)i + (0.6 \times 2)j = 0.5i + 1.2j \text{Therefore:} v = (4i - 5j) + (0.5i + 1.2j) = 4.5i - 3.8j \text{From solution: } v = 4.5i - 4.6j \text{Answer: option (3)}

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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
}