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 figure shows the graph of the $x$-coordinate of a particle moving along the $x$-axis as a function of time. The average velocity during $t=0$ to $6 \,s$ and the instantaneous velocity at $t=3 \,s$ respectively,will be

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?

An object is moving with variable speed,then

The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in the figure.
$(A)$ $A$ lives closer to the school.
$(B)$ $B$ lives closer to the school.
$(C)$ $A$ takes less time to reach home.
$(D)$ $A$ travels faster than $B$.
$(E)$ $B$ travels faster than $A$.
Choose the correct answer from the options given below:

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