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 following figures show velocity $v$ versus time $t$ curves. But only some of these can be realized in a particle. These are:

In the picture shown,a ball starting from rest rolls down a ramp $AB$,moves along the horizontal bottom $BC$,then goes up a smaller ramp $CD$,and thereafter rolls on the horizontal plane $DE$. Ignore friction and air resistance. Which of the following figures shows the variation in speed with time?

The position $x$ of a particle with respect to time $t$ along the $x$-axis is given by $x = 9t^2 - t^3$,where $x$ is in metres and $t$ is in seconds. What will be the position of this particle when it achieves maximum speed along the $x$-direction?

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. The ratio of their velocities is

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