The position $x$ of a particle varies with time $t$ as $x = ct^2 + b$,where $c$ and $b$ are positive constants. Which of the following graphs is correct?

The relation between velocity $v$ and displacement $x$ is $v = x^2$. Find the acceleration at $x = 3 \ m$.

The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time-axis as shown in the figure. The ratio of their respective velocities is:

Consider a car initially at rest,starts to move along a straight road first with acceleration $5 \ m \ s^{-2}$,then with uniform velocity and finally,decelerating at $5 \ m \ s^{-2}$,before coming to a stop. Total time taken from start to end is $t = 25 \ s$. If the average velocity during that time is $72 \ km \ hr^{-1}$,the car moved with uniform velocity for a time of: (in $s$)

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$)