The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $6 \, s$ are respectively:

The position of a particle related to time is given by $x = (5t^2 - 4t + 5) \, m$. The magnitude of velocity of the particle at $t = 2 \, s$ will be $........... \, ms^{-1}$.

Let us define a motion as $A$ when velocity is positive and increasing,$A^{-1}$ when velocity is negative and increasing,$R$ when velocity is positive and decreasing,and $R^{-1}$ when velocity is negative and decreasing. Now,match the following two columns for the given $s-t$ graph.

Column $I$	Column $II$
$(A)$ $M$	$(p)$ $A^{-1}$
$(B)$ $N$	$(q)$ $R^{-1}$
$(C)$ $P$	$(r)$ $A$
$(D)$ $Q$	$(s)$ $R$

What is the acceleration of the particle on $OA$,$AB$,and $BC$ respectively?

The velocity-time graph for a particle moving along the $x$-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by

$A$ body starts from rest and travels a distance $S$ with uniform acceleration,then moves uniformly a distance $2S$ and finally comes to rest after moving further $3S$ under uniform retardation. The ratio of the average velocity to maximum velocity is