$A$ body moves according to the formula $v = 1 + t^2$,where $v$ is the velocity at time $t$. The acceleration after $3 \text{ s}$ will be .......... $\text{cm/s}^2$. ($v$ is in $\text{cm/s}$)

The distance $s$ in meters covered by a body in $t$ seconds is given by $s = 3t^2 - 8t + 5$. The body will stop after

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm/sec}$. The rate at which the area increases,when the side is $10 \text{ cm}$,is

$A$ bullet is shot horizontally and its distance $S$ cm at time $t$ second is given by $S=1200t-15t^2$. Then, the distance covered by the bullet when it comes to rest is: (in $\text{ cm}$)

If the rate of increase of the radius of a circle is $5 \text{ cm/sec}$, then the rate of increase of its area, when the radius is $20 \text{ cm}$, will be

Water is dripping out at a steady rate of $1 \text{ cm}^3/\text{sec}$ through a tiny hole at the vertex of a conical vessel,whose axis is vertical. When the slant height of water in the vessel is $4 \text{ cm}$,find the rate of decrease of the slant height,where the semi-vertical angle of the conical vessel is $\frac{\pi}{6}$.