Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

$A$ block of mass $10 \, kg$,moving in $x$ direction with a constant speed of $10 \, m/s$,is subjected to a retarding force $F = 0.1 \, x \, N$ during its travel from $x = 20 \, m$ to $30 \, m$. Its final $KE$ will be ............... $J$.

Power applied to a particle varies with time as $P = (4t^3 - 5t + 2) \, W$,where $t$ is in seconds. Find the change in its $K.E.$ between time $t = 2 \, s$ and $t = 4 \, s$. ............... $J$

$A$ force $\overrightarrow F = - K(y\hat i + x\hat j)$ (where $K$ is a positive constant) acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle is taken along the positive $x$-axis to the point $(a, 0)$ and then parallel to the $y$-axis to the point $(a, a)$. The total work done by the force $\overrightarrow F$ on the particle is

The kinetic energy $(E_k)$ of a particle moving along the $X$-axis varies with its position $(X)$ as shown in the figure. The force acting on the particle at $X = 10 \ m$ is

$A$ force acts on a $3.0 \ g$ particle in such a way that the position of the particle as a function of time is given by:
$x = 3t - 4t^2 + t^3$
Where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \ s$ is ................. $mJ$