A particle is moving along the x-axis with its position varying with time as x = αt⁴ + βt² + γt + δ. The ratio of its initial velocity to its initial acceleration, respectively, is:
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A particle is moving along the x-axis with its position varying with time as x = αt⁴ + βt² + γt + δ. The ratio of its initial velocity to its initial acceleration, respectively, is:

G1 Physics · Accepted Answer

Step 1: v = dx/dt = 4αt³ + 2βt + γ. Thus v(0)=γ. Step 2: a = dv/dt = 12αt² + 2β. Thus a(0)=2β. Step 3: Therefore v(0):a(0) = γ:2β. Final answer: D.