If $t = \sqrt{x} + 4$,then $\left(\frac{dx}{dt}\right)_{t=4}$ is:

The given graph shows the variation of velocity $v$ with displacement $x$. Which one of the graphs given below correctly represents the variation of acceleration $a$ with displacement $x$?

The figure shows the position of a particle moving on the $x$-axis as a function of time.

The displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

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.