Import Question JSON

Current Question (ID: 19050)

Question:

$\text{The position } x \text{ of a particle moving along the } x\text{-axis varies with time } t \text{ according to the equation: } x = 2.5t^2. \text{ What is the speed of the particle at } t = 5 \text{ s?}$

Options:

1. $5 \text{ m/s}$
2. $10 \text{ m/s}$
3. $25 \text{ m/s}$
4. $50 \text{ m/s}$

Solution:

$\text{Hint: } v = \frac{dx}{dt}$ $\text{Step 1: Find the speed of the particle.}$ $x = 2.5t^2$ $\text{Differentiate above equation with respect to } t :$ $v = \frac{dx}{dt}$ $\Rightarrow v = \frac{d(2.5t^2)}{dt} = 5t$ $\Rightarrow v = 5t$ $\text{Step 2: Put } t = 5 \text{ s. to get the speed of the particle at } t = 5 \text{ s.}$ $\Rightarrow v = 25 \text{ m/s.}$ $\text{Hence, option (3) is the correct answer.}$

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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
}