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Physics · MOTION IN A STRAIGHT LINE
हिन्दीCar A moves along a straight road with constant velocity \( v_A = 20 \text{ m/s} \). Car B is initially a distance \( d = 150 \text{ m} \) ahead of Car A. At \( t = 0 \), Car B starts from rest and accelerates in the same direction with constant acceleration \( a_B = 2.0 \text{ m/s}^2 \). Find the minimum distance of approach between the two cars.
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Correct answer · Option C
\( 50 \text{ m} \)
Explanation
Positions: \( x_A(t) = 20 t \) and \( x_B(t) = 150 + t^2 \). Separation \( S(t) = x_B(t) - x_A(t) = 150 + t^2 - 20 t \). Minimum separation occurs when relative velocity is zero: \( \frac{dS}{dt} = 2t - 20 = 0 \implies t = 10 \text{ s} \). Minimum distance \( S_{\min} = 150 + 100 - 200 = 50 \text{ m} \).
