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Physics · MOTION IN A STRAIGHT LINE
हिन्दीA particle moves along a straight line with uniform acceleration \( a \). Its velocities at two points A and B are \( v_A = 10 \text{ m/s} \) and \( v_B = 30 \text{ m/s} \) respectively. Calculate the velocity of the particle as it passes through the midpoint C of the segment AB.
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Correct answer · Option A
\( 10\sqrt{5} \text{ m/s} \)
Explanation
Let distance AB be \( s \). Then \( v_C^2 - v_A^2 = 2 a (s/2) = a s \) and \( v_B^2 - v_C^2 = 2 a (s/2) = a s \). Thus \( v_C^2 = \frac{v_A^2 + v_B^2}{2} = \frac{100 + 900}{2} = 500 \implies v_C = \sqrt{500} = 10\sqrt{5} \text{ m/s} \).
