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

The area $A$ of a blot of ink is growing such that after $t$ seconds its area is given by $A = (3t^2 + 7) \, cm^2$. Calculate the rate of increase of area at $t = 2 \, s$. .......... $cm^2/s$

The acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in the figure. The corresponding velocity-time graph would be:

The accompanying graph of position $x$ versus time $t$ represents the motion of a particle. If $p$ and $q$ are both positive constants,the expression that best describes the acceleration $a$ of the particle is

What does $\dot x$ represent?

In the following velocity-time graph,the distance travelled by the body in metres is ............. $m$.