The work done in moving an object from the origin to a point whose position vector is $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$ is:

$A$ force of $(5\hat i + 6\hat j - 7\hat k) \, N$ is applied to a body of mass $10 \, kg$,causing it to displace from position $(4\hat i - 2\hat j + 5\hat k) \, m$ to $(8\hat i + 6\hat j - 3\hat k) \, m$. Calculate the work done in $J$.

At time $t=0$,a particle starts moving along the $x$-axis. If its kinetic energy increases uniformly with time $t$,the net force acting on it must be proportional to

$A$ body of mass $50 \ kg$ is lifted to a height of $20 \ m$ from the ground in two different ways as shown in the figure. The ratio of work done against gravity in both the respective cases will be:

Consider a particle on which constant forces $F_{1}=\hat{i}+2 \hat{j}+3 \hat{k} \text{ N}$ and $F_{2}=4 \hat{i}-5 \hat{j}-2 \hat{k} \text{ N}$ act together, resulting in a displacement from position $r_{1}=20 \hat{i}+15 \hat{j} \text{ cm}$ to $r_{2}=7 \hat{k} \text{ cm}$. The total work done on the particle is:

$A$ 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?