The displacement and the increase in the velocity of a moving particle in the time interval of $$t$$ to $$(t+1) \mathrm{s}$$ are $$125 \mathrm{~m}$$ and $$50 \mathrm{~m} / \mathrm{s}$$, respectively. The distance travelled by the particle in $$(\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}$$ is _________ m.

A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimum velocity $$u$$ with which that ball just hits the step 5 of the stairway will be $$\sqrt{x} \mathrm{~ms}^{-1}$$ where $$x=$$ __________ [use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ ].

A body falling under gravity covers two points $$A$$ and $$B$$ separated by $$80 \mathrm{~m}$$ in $$2 \mathrm{~s}$$. The distance of upper point A from the starting point is _________ $$\mathrm{m}$$ (use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$).

A particle starts from origin at $$t=0$$ with a velocity $$5 \hat{i} \mathrm{~m} / \mathrm{s}$$ and moves in $$x-y$$ plane under action of a force which produces a constant acceleration of $$(3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2$$. If the $$x$$-coordinate of the particle at that instant is $$84 \mathrm{~m}$$, then the speed of the particle at this time is $$\sqrt{\alpha} \mathrm{~m} / \mathrm{s}$$. The value of $$\alpha$$ is _________.