The distance $s$ in meters covered by a particle in $t$ seconds is given by $s = 2 + 27t - t^3$. The particle will stop after covering a distance of:

$A$ particle is moving on a straight line. The distance $S$ travelled in time $t$ is given by $S = at^2 + bt + 6$. If the particle comes to rest after $4 \text{ s}$ at a distance of $16 \text{ m}$ from the starting point,then the acceleration of the particle is:

The equation of motion of a stone thrown vertically upward from the surface of a planet is given by $s = 10t - 3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$ respectively. The stone will return to the surface of the planet after:

If the surface area of a spherical bubble is increasing at the rate of $4 \text{ cm}^2/\text{sec}$,then the rate of change in its volume (in $\text{cm}^3/\text{sec}$) when its radius is $8 \text{ cm}$ is:

In a Maha Kumbh, a drone camera is moving along the curve $3y = x^3 - 3$. The camera captures high-quality pictures when the $y$-coordinate changes $9$ times as fast as the $x$-coordinate. Which of the following is a precise position of the drone at that instant?

If the distance travelled by a point in time $t$ is $s = 180t - 16t^2$,then the rate of change in velocity is ......... $unit$.