The distance $(s)$ travelled by a particle in time $t$ is given by $s = 4t^2 + 2t + 3$. The velocity of the particle when $t = 3$ seconds is

$A$ ladder $5 \ m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/sec$. How fast is its height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?

The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm s}^{-1}$. How fast does its area increase when its side is $10 \text{ cm}$?

The radius of a sphere increases at the rate of $0.04 \text{ cm/sec}$. The rate of increase in the volume of that sphere with respect to its surface area,when its radius is $10 \text{ cm}$ is

If the distance $s$ traveled by a particle in time $t$ is $s = a \sin t + b \cos 2t$,then the acceleration at $t = 0$ is