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

Two trains, which are moving along different tracks in opposite directions, are put on the same track by mistake. On noticing the mistake, when the trains are $300 \, m$ apart, the drivers start slowing down the trains. The graphs given below show the decrease in their velocities as a function of time. The separation between the trains when both have stopped is: (in $ \, m$)

The area $A$ of a blot of ink is growing such that after $t$ seconds its area is given by $A = (3t^2 + 7) \, cm^2$. Calculate the rate of increase of area at $t = 2 \, s$. .......... $cm^2/s$

The position of an object moving along the $x$-axis is given by $x = a + b t^{2}$,where $a = 8.5 \; m$,$b = 2.5 \; m s^{-2}$,and $t$ is measured in seconds. What is the velocity at $t = 0 \; s$ and $t = 2.0 \; s$?

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.

The figure shows a velocity-time graph of a particle moving along a straight line. The total distance travelled by the particle is ........ $m$.