A motorist starting a car from rest accelerates uniformly to a speed of $v\, m/s$ in $9\, seconds$. He maintains this speed for another $50\, seconds$ and then applies the brakes and decelerates uniformly to rest. His deceleration is numberically equal to three times his previous acceleration. Then the time during which the deceleration takes place is ..........$s$ :-

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 motor car moving with a uniform speed of $20\,m/\sec $ comes to stop on the application of brakes after travelling a distance of $10\,m$ Its acceleration is..........$m/{\sec ^2}$

A small block slides without friction down an inclined plane starting from rest. Let ${S_n}$be the distance travelled from time $t = n - 1$ to $t = n.$ Then $\frac{{{S_n}}}{{{S_{n + 1}}}}$ is

The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be

Relation between velocity and displacement is $v = x^2$. Find acceleration at $x = 3m$ :- ............. $\mathrm{m/s}^{2}$