The figure shows the displacement of a particle moving along the $X-$axis as a function of time. The force acting on the particle is zero in the region:

The accompanying graph of position $x$ versus time $t$ represents the motion of a particle. If $p$ and $q$ are both positive constants,the expression that best describes the acceleration $a$ of the particle is

The figure shows the position-time $(x-t)$ graph of the motion of two boys $A$ and $B$ returning from school $O$ to their homes $P$ and $Q$ respectively. Which of the following statements is true?

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

The distance travelled by an object in time $t$ is given by $s = 2.5 t^2$. The instantaneous speed of the object at $t = 5\,s$ will be $....\,m/s$.

Figures $(i)$ and $(ii)$ below show the displacement-time graphs of two particles moving along the x-axis. We can say that