$A$ particle gets displaced by $\Delta \vec{r} = (2\hat{i} + 3\hat{j} + 4\hat{k}) \text{ m}$ under the action of a force $\vec{F} = (7\hat{i} + 4\hat{j} + 3\hat{k}) \text{ N}$. The change in its kinetic energy is ............... $\text{J}$.

Given that $W = \vec F \cdot \vec s = 0$ and $F \neq 0, s \neq 0$,then

$A$ body constrained to move along the $y$-axis is subjected to a constant force $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$. The work done by this force in moving the body a distance of $4 \text{ m}$ along the $y$-axis is ............... $J$.

When an object is dragged $10 \, m$ along a road,a frictional force of $200 \, N$ acts in the direction opposite to its motion. What is the work done by the frictional force on the object (in $, J$)?

$A$ man carries a bucket of weight $60 \ N$ and walks $7 \ m$ in the horizontal direction,then climbs $5 \ m$ in the vertical direction. What is the work done by the man in $J$?

The figure shows a mass $m$ on a frictionless surface. It is connected to a rigid wall by means of a massless spring of spring constant $k$. Initially,the spring is at its natural position. If a force of constant magnitude $F$ starts acting on the block towards the right,then the speed of the block when the deformation in the spring is $x$ will be