Question

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:

• A. $2\alpha : \delta$
• B. $\gamma : 2\delta$
• C. $4\alpha : \beta$
• D. $\gamma : 2\beta$

Answer 1

Answer: (D)

$\gamma : 2\beta$

Answer 2

Velocity (v) = $\frac{dx}{dt} = 4\alpha t^3 + 2\beta t + \gamma$ Initial velocity (at t = 0) = γ

Acceleration (a) = $\frac{dv}{dt} = 12\alpha t^2 + 2\beta$ Initial acceleration (at t = 0) = 2β

Ratio of initial velocity to initial acceleration = $\frac{\gamma}{2\beta}$