A particle moves for $8\, seconds$. It first accelerates from rest and then retards to rest. If the retardation be $3\, times$ the acceleration, then time for which it accelerates will be 

An automobile travelling with a speed of $60\,\,km/h,$ can brake to stop within a distance of $20 \,m$. If the car is going twice as fast, i.e. $120\, km/h$, the stopping distance will be  ........... $m$

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

Position $x$ of a particle at any instant is related with velocity as $v = \sqrt {2x + 9}$ . The particle starts from origin. Then initial acceleration and velocity are