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 $x$?

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

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

Two cars $A$ and $B$ start from a point at the same time in a straight line and their positions are represented by $R_{A}(t) = at + bt^2$ and $R_{B}(t) = xt - t^2$. At what time do the cars have the same velocity?

The distance travelled by a particle is related to time $t$ as $x = 4t^2$. The velocity of the particle at $t = 5 \, s$ is $......... \, ms^{-1}$.

The $x-t$ graph of a particle moving along a straight line is shown in the figure. The speed-time graph of the particle is correctly shown by: