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Current Question (ID: 8927)

Question:

$\text{A car } A \text{ is traveling on a straight level road at a uniform speed of 60 km/h. It is followed by another car } B \text{ which is moving at a speed of 70 km/h. When the distance between them is 2.5 km, car } B \text{ is given a deceleration of 20 km/h}^2\text{. After how much time will car } B \text{ catch up with car } A\text{?}$

Options:

1. $1 \text{ hr}$
2. $\frac{1}{2} \text{ hr}$
3. $\frac{1}{4} \text{ hr}$
4. $\frac{1}{8} \text{ hr}$

Solution:

$\text{Hint: Use the concept of relative motion.}$ $\text{Step 1: Draw the diagram.}$ $\text{Car B is at 70 km/h and car A is at 60 km/h, separated by 2.5 km initially.}$ $\text{Step 2: From the frame of reference of A:}$ $\text{Initial relative velocity of B w.r.t A = 70 - 60 = 10 km/h}$ $\text{Relative acceleration of B w.r.t A = -20 km/h}^2$ $\text{Initial relative distance = 2.5 km}$ $\text{Step 3: Use the equations of motion.}$ $\text{The final velocity of car B w.r.t car A:}$ $v^2 = (10)^2 - 2 \times 20 \times 2.5 = 0$ $\text{The time taken by car B to catch car A:}$ $v = u + at$ $\text{or } 0 = 10 - 20t$ $\text{or } t = \frac{1}{2}h$ $\text{Hence, option (2) is the correct answer.}$

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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
}