What is stopping distance ?

A body moves on a frictionless plane starting from rest. If $\mathrm{S}_{\mathrm{n}}$ is distance moved between $\mathrm{t}=\mathrm{n}-1$ and $\mathrm{t}$ $=\mathrm{n}$ and $\mathrm{S}_{\mathrm{n}-1}$ is distance moved between $\mathrm{t}=\mathrm{n}-2$ and $t=n-1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1-\frac{2}{x}\right)$ for $n$ $=10$. The value of $x$ is

A bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet, when the velocity is doubled, will be

Speed-time graph of two cars $A$ and $B$ approaching towards each other is shown in figure. Initial distance between them is $60\,m$. The two cars will cross each other after time $..........\,s$

A particle starts from rest at $x=0\; m$ with an acceleration of $1 \,m / s ^2$. At $t = 5\;s _{ s }$ it receives an additional acceleration in the same direction as its motion. At $t =10\; s$ its speed and position are $v$ and $x$, respectively. Had the additional acceleration not been provided, its speed and position would have been $v _0$ and $x _0$, respectively. It is found that $x - x _0$ is $12.5 \,m$. Then one can conclude that $v - v _0$ is .............. $\,m / s$