An object is dropped from a certain point A at a height ' h ' from the ground. During it's journey straight downwards, the object passes points $B$ and $C$ such that the ratio of time taken $t_1$ to cover $A B$ and $t_2$ to cover $B C$ is $1:(\sqrt{2}-1)$. What is the ratio of distances $A B: B C$ ?

A car, starting from rest, accelerates at a rate of $\beta$ through a distance S , then continues at constant speed for time t and then decelerates at a rate of $\frac{\beta}{2}$ to come to rest. If the total distance travelled is $10 S$, then ratio $\frac{S}{t^2}$ is

From the same point, two stones A and B are thrown simultaneously, A is thrown up vertically with a velocity of $10 \mathrm{~ms}^{-1}$ and $B$ is thrown up with the same velocity at $30^{\circ}$ with the horizontal. The separation between the balls at 2 s is