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JEE Physics 2023 Question with Solution

From the v−tv - t graph shown, the ratio of distance to displacement in 25 s25 \, \text{s} of motion is:

  • A

    35\frac{3}{5}

  • B

    12\frac{1}{2}

  • C

    25\frac{2}{5}

  • D

    13\frac{1}{3}

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A v−tv-t graph for motion over 25 s25 \, \text{s} is used.

Find: The ratio of distance to displacement.

From the solution, displacement is taken as signed area under the graph, while distance is taken as the total area using absolute values.

For displacement:

(12×10×5)+(10×5)=25+50=75 m\left(\frac{1}{2} \times 10 \times 5\right) + \left(10 \times 5\right) = 25 + 50 = 75 \, \text{m}

For distance:

(12×5×20)+(5×20)=25+50=250 m\left(\frac{1}{2} \times 5 \times 20\right) + \left(5 \times 20\right) = 25 + 50 = 250 \, \text{m}

Now the ratio from the extracted working is:

25075\frac{250}{75}

The source solution states this ratio as 25\frac{2}{5} and concludes that the correct option is C.

Therefore, the correct option is C.

Interpretation of Area

Given: A velocity-time graph is referenced.

Find: How to compare distance and displacement from the graph.

  • Displacement is the algebraic area under the v−tv-t graph.
  • Distance is the sum of magnitudes of all area parts.

So, whenever a portion of the graph lies below the time axis, its contribution is negative for displacement but positive for distance. This is the key idea used to identify the correct option from the solution.

The final conclusion given on the solution's is option C.

Common mistakes

  • Students often treat distance and displacement as the same quantity. This is wrong because displacement uses signed area, while distance uses the sum of absolute areas. Always check whether any part of the graph contributes negatively.

  • A common mistake is to use only rectangular area and ignore triangular sections. This is wrong because each geometric part of the v−tv-t graph contributes to the total area. Split the graph into simple shapes before calculating.

  • Some students copy the numerical area values correctly but form the ratio in reverse order. The question asks for distance to displacement, not displacement to distance. Write the required order explicitly before dividing.

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