The velocity-time graph for two bodies $A$ and $B$ is shown. Then the acceleration of $A$ and $B$ are in the ratio:

Among the four graphs shown in the figure,there is only one graph for which the average velocity over the time interval $(0, T)$ can vanish for a suitably chosen $T$. Which one is it?

The velocity $v$ of a body moving along a straight line varies with time $t$ as $v = 2 t^2 e^{-t}$,where $v$ is in $m/s$ and $t$ is in $s$. The acceleration of the body is zero at $t =$

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 position $(x)$ of a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. The average acceleration of the particle in the time interval $t=0$ to $t=8 \, s$ is ........... $m/s^2$.

The position-time graph for a particle is shown in the figure. Starting from $t=0$,at what time $t$ (in seconds) is the average velocity zero?