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

From the $v-t$ graph,find the total distance covered by the car in time $t = t_1 + t_2$.

The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and the maximum possible retardation is $5\ m/s^2$. If the maximum achievable speed of the train is $10\ m/s$,then the minimum time in which the train can complete a journey of $135\ m$ starting from rest and ending at rest is.........$s$.

$A$ particle starts from rest and moves in a straight line. It travels a distance $2L$ with uniform acceleration and then moves with a constant velocity for a further distance of $L$. Finally,it comes to rest after moving a distance of $3L$ under uniform retardation. Then the ratio of average speed to the maximum speed $\left(\frac{\bar{V}}{V_m}\right)$ of the particle is

The velocity-time graph of a body is shown in the figure. It implies that at point $B$

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.