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Q18 (NDA-II/2013) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Data interpretation graphs Answer Verified

The plot given above represents the velocity of a particle (in m/s) with time (in seconds). Assuming that the plot represents a semi-circle, distance traversed by the particle at the end of 7 seconds is approximately

Result
Your answer: —  Â·  Correct: A
Explanation

The distance traversed by a particle is represented by the area under its velocity-time (v-t) graph. For a semicircular v-t plot where the time axis (x-axis) spans from 0 to 7 seconds, the diameter of the semicircle is 7 units (seconds). Consequently, the radius (r) of this semicircle is 3.5 units. The area of a semicircle is calculated using the formula A = (1/2)πr². Substituting the radius, we get Area = (1/2) * π * (3.5)². Using the approximation π ≈ 3.14159, the calculation becomes 0.5 * 3.14159 * 12.25, which equals approximately 19.24. Among the given options, 19 m is the closest approximation to the calculated area. This confirms that the total distance covered by the particle at the end of the 7-second interval is approximately 19 m.

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