The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and the maximum possible retardation is $5\ m/s^2$. If the maximum achievable speed of the train is $10\ m/s$,then the minimum time in which the train can complete a journey of $135\ m$ starting from rest and ending at rest is.........$s$.

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure,for a time interval of $40 \text{ s}$. The total distance travelled by the particle and the average velocity during this period are,respectively . . . . . . .

What is the ratio of the velocity in the first $1 \ s$ to the velocity in the next $2 \ s$ based on the given displacement-time graph?

The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in the figure.
$(A)$ $A$ lives closer to the school.
$(B)$ $B$ lives closer to the school.
$(C)$ $A$ takes less time to reach home.
$(D)$ $A$ travels faster than $B$.
$(E)$ $B$ travels faster than $A$.
Choose the correct answer from the options given below:

The figure shows a velocity-time graph of a particle moving along a straight line. Identify the region in which the magnitude of the rate of change of velocity $\left| \frac{\Delta \vec{v}}{\Delta t} \right|$ of the particle is maximum.

The distance covered by the particle in the last $2\,s$ is what fraction of the total distance covered by it in $7\,s$?