$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

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

The distance travelled by a particle moving in a straight line in time $t$ is $s = \sqrt{at^2 + bt + c}$. The acceleration of the particle is

$A$ rod of length $41 \ ft$ with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \ ft/min$. When the end $B$ is at a height of $9 \ ft$ from the floor, the rate at which the area of the triangle formed by the rod with the wall and the floor changes at that instant is (in $ft^2/min$):

If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then find the rate of change of its volume with respect to $x$.

The interval in which the function $f(x) = x^3$ increases less rapidly than $g(x) = 6x^2 + 15x + 5$ is: