The distance travelled $s$ (in $cm$) by a particle in $t$ seconds is given by $s = t^3 + 2t^2 + t$. The speed of the particle after $1$ second will be ......... $cm/sec$.

The equation of motion of a particle is given by $s = 2t^3 - 9t^2 + 12t + 1$,where $s$ and $t$ are measured in $cm$ and $sec$. The time when the particle stops momentarily is

In $\Delta ABC$,sides $a$ and $b$ are kept constant such that there is an error $\alpha$ in angle $C$. What is the relative error in the area?

$A$ particle moves according to the law $s=t^{3}-6t^{2}+9t+25$. Find the displacement of the particle when its velocity is zero. (in $\text{ units}$)

$A$ particle is moving on a straight line,where its position $s$ (in metre) is a function of time $t$ (in seconds) given by $s = at^2 + bt + 6, t \ge 0$. If it is known that the particle comes to rest after $4 \, s$ at a distance of $16 \, m$ from the starting position $(t = 0)$,then the retardation in its motion is

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is