A particle is moving along $x$-axis with its position ( x ) varying with time ( t ) as $x=\alpha {t}^{4}+\beta {t}^{2}+\gamma t+\delta$. The ratio of its initial velocity to its initial acceleration, respectively, is:

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Correct answer: d) $\gamma :2\beta$. Find initial velocity (v₀) and initial acceleration (a₀) from the position equation x(t). x = αt⁴ + βt² + γt + δ. Velocity v = dx/dt = 4αt³ + 2βt + γ. Initial velocity v₀ (at t=0) = γ. Acceleration a = dv/dt = 12αt² + 2β. Initial acceleration a₀ (at t=0) = 2β. Ratio v₀ : a₀ = γ : 2β.

A particle is moving along \(x\)-axis with its position ( x ) varying with time ( t ) as \(x=\alpha {t}^{4}+\beta {t}^{2…

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