The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is

$A$ particle starts from the origin at time $t = 0$ and moves along the positive $x-$ axis. The velocity-time graph is shown in the figure. What is the position of the particle at time $t = 5\,s$ (in $,m$)?

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:

$A$ steel ball is released from rest a distance above a rigid horizontal surface and bounces several times. The diagram shows how its velocity varies with time. Which statement correctly explains why the areas $X$ and $Y$ are equal?

The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?

The variation of velocity of a particle moving along a straight line with time is illustrated in the following figure. The distance travelled by the particle in $4 \, s$ is: (in $, m$)