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Current Question (ID: 8899)

Question:

$\text{The velocity-time } (v-t) \text{ graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 s are, respectively:}$ $\text{The graph shows:}$ $\text{- From } t = 0 \text{ to } t = 2\text{s: } v = 4\text{ m/s}$ $\text{- From } t = 2 \text{ to } t = 4\text{s: } v = -2\text{ m/s}$ $\text{- From } t = 4 \text{ to } t = 6\text{s: } v = 2\text{ m/s}$

Options:

1. $8\text{ m, } 16\text{ m}$
2. $16\text{ m, } 8\text{ m}$
3. $16\text{ m, } 16\text{ m}$
4. $8\text{ m, } 8\text{ m}$

Solution:

$\text{Hint: The area under the V-t graph gives displacement covered by the body.}$ $\text{Step: Find the distance and displacement covered by the body.}$ $\text{Displacement = Sum of all the area with sign}$ $= (A_1) + (-A_2) + (A_3) = (2 \times 4) + (-2 \times 2) + (2 \times 2)$ $\therefore \text{Displacement} = 8\text{ m}$ $\text{Distance = Sum of all the areas without sign}$ $= |A_1| + |-A_2| + |A_3| = |8| + |-4| + |4| = 8 + 4 + 4$ $\therefore \text{Distance} = 16\text{ m}$ $\text{Therefore, the distance covered by the body is 16 m, and the displacement covered by the body is 8 m.}$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

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
}