$A$ 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 ............... $J$.

The kinetic energy $(KE)$ acquired by a mass $m$ in travelling a certain distance $d$,starting from rest,under the action of a constant force $F$ is ..........

$A$ small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} \text{ N}$. The value of work done will be $............ \text{ J}$.

Two persons $A$ and $B$ perform the same amount of work in moving a body through a certain distance $d$ with the application of forces acting at angles $45^{\circ}$ and $60^{\circ}$ with the direction of displacement,respectively. The ratio of the force applied by person $A$ to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is ...... .

$A$ man of mass $50 \ kg$ carrying a load of $10 \ kg$ reaches the top of a building in $4 \ minutes$. The work done by the man is $6 \times 10^4 \ J$. If he reaches the top in $2 \ minutes$,the work done by the man will be:

$A$ body of mass $m$ starts from rest and acquires a velocity $v$ in time $t_1$. The work done in time $t$ is proportional to: