$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

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

$A$ 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 $\text{ cm}$)

The displacement $S$ of a moving particle at a time $t$ is given by $S=5+\frac{48}{t}+t^3$. Then its acceleration when the velocity is zero,is

At present,a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ with respect to the additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs $25$ more workers,then the new level of production of items is:

The area of a square increases at the rate of $0.5 \text{ cm}^2/\text{sec}$. The rate at which its perimeter is increasing when the side of the square is $10 \text{ cm}$ long,is