A constant force of \[ \mathbf{F} = (8\hat{i} - 2\hat{j} + 6\hat{k}) \text{ N} \] acts on a body of mass 2 kg, displacing it from \[ \mathbf{r_1} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ m to } \mathbf{r_2} = (4\hat{i} - 3\hat{j} + 6\hat{k}) \text{ m}. \] The work done in the process 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: