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Current Question (ID: 19041)

Question:

$\text{What will be the velocity of the particle if the position of the particle is given by;} \; x = 2t^2 \; \text{at} \; t = 2 \; \text{s?}$

Options:

1. $8 \; \text{m/s}$
2. $4 \; \text{m/s}$
3. $16 \; \text{m/s}$
4. $32 \; \text{m/s}$

Solution:

$\text{Hint:} \; v(t) = \frac{dx}{dt}$ $\text{Step: Find the velocity of the particle.}$ $\text{The velocity} \; v(t) \; \text{is the first derivative of the position function is given by;} \; \Rightarrow v(t) = \frac{dx}{dt}$ $\text{Differentiating} \; x(t) = 2t^2 \; \text{we get;} \; \Rightarrow v(t) = \frac{d}{dt} (2t^2) = 4t$ $\text{Now, substitute} \; t = 2 \; \text{seconds into the velocity equation we get;} \; \Rightarrow v(2) = 4 \times 2 = 8 \; \text{m/s}$ $\text{Hence, option} \; (1) \; \text{is the correct answer.}$

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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
}