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Physics · MOTION IN A STRAIGHT LINE
हिन्दीA particle moves along the x-axis such that its acceleration at time \( t \) is given by \( a(t) = (3t - 2)\text{ m s}^{-2} \). At \( t = 0 \), the position of the particle is \( x = 2\text{ m} \) and its velocity is \( v = 4\text{ m s}^{-1} \). What is the position of the particle at \( t = 4\text{ s} \)?
Correct answer · Option 3
\( 34\text{ m} \)
Explanation
Velocity \( v(t) = \int (3t-2) dt + 4 = \frac{3}{2}t^2 - 2t + 4 \). Position \( x(t) = \int (\frac{3}{2}t^2 - 2t + 4) dt + 2 = \frac{1}{2}t^3 - t^2 + 4t + 2 \). At \( t=4 \), \( x(4) = 32 - 16 + 16 + 2 = 34\text{ m} \).
