The motion of a particle is described by the equation $x = a + b{t^2}$ where $a = 15\, cm$ and $b = 3 \,cm/s^2$. Its instantaneous velocity at time $3\, sec$ will be……..$cm/sec$

A man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance $d$ from highway (point $M$ ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance $RM$, so that the time taken to reach $P$ is minimum?

The graph shows the variation of velocity of a rocket with time. Then, the maximum height attained by the rocket is ………..$km$ :-

What does $\dot x$ represent ?

The velocity of a particle is  $v=v_0 +gt+ft^2$. If its position is $x= 0$ at $t= 0 $, then its displacement after unit time ($t= 1$) is