A force defined by $ F = \alpha t^2 + \beta t $ acts on a particle at a given time $ t $. The factor which is dimensionless, if $ \alpha $ and $ \beta $ are constants, is:
At a given temperature and pressure, the equilibrium constant values for the equilibria are given below:
$ 3A_2 + B_2 \rightleftharpoons 2A_3B, \, K_1 $
$ A_3B \rightleftharpoons \frac{3}{2}A_2 + \frac{1}{2}B_2, \, K_2 $
The relation between $ K_1 $ and $ K_2 $ is:
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: