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Physics · MOTION IN A STRAIGHT LINE
हिन्दीThe position \( x \) of a particle moving along a straight line varies with time \( t \) as \( x = 2t^3 - 9t^2 + 12t + 5 \) (where \( x \) is in meters and \( t \) in seconds). The velocity of the particle when its acceleration becomes zero is:
Correct answer · Option 3
\( -1.5\text{ m/s} \)
Explanation
\( v = \frac{dx}{dt} = 6t^2 - 18t + 12 \). Acceleration \( a = \frac{dv}{dt} = 12t - 18 \). Setting \( a = 0 \implies t = 1.5\text{ s} \). Substituting \( t = 1.5\text{ s} \) into velocity equation: \( v(1.5) = 6(2.25) - 18(1.5) + 12 = 13.5 - 27 + 12 = -1.5\text{ m/s} \).
