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

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

$A$ scooter accelerates from rest for time $t_{1}$ at a constant rate $a_{1}$ and then retards at a constant rate $a_{2}$ for time $t_{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be ..... .

Can the position-time graph of a moving object be parallel to the position axis? Why?

The graph of an object's motion (along the $x-$ axis) is shown in the figure. The instantaneous velocity of the object at points $A$ and $B$ are $v_A$ and $v_B$ respectively. Then

Suggest a suitable physical situation for the following $x-t$ graph.