$A$ ball is dropped from the top of a tower. What is the ratio of the work done by the force of gravity during the $1^{st}$,$2^{nd}$,and $3^{rd}$ seconds?

$A$ particle moves from position $3\hat i + 2\hat j - 6\hat k$ to $14\hat i + 13\hat j + 9\hat k$ due to a uniform force of $(4\hat i + \hat j + 3\hat k) \, N$. If the displacement is in meters,the work done will be ......... $J$.

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

$A$ force $\vec F = (5\hat i + 3\hat j) \text{ N}$ is applied to a particle,which displaces it from its origin to the point $\vec r = (2\hat i - 1\hat j) \text{ m}$. The work done on the particle is ........... $J$.

$A$ 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 $............ \text{ J}$.

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by