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 ..........$s$ :-

The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be

A car is moving with velocity $V$. If stop after applying break at a distance of $20\; m$. If velocity of car is doubled, then how much distance it will cover (travel) after applying break

The area under acceleration-time graph gives

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 .............. $\,m / s$

A particle moves towards east with velocity $5\, m/s$. After $10$ seconds its direction changes towards north with same velocity. The average acceleration of the particle is