$A$ ship of mass $3 \times 10^7 \, kg$ initially at rest is pulled by a force of $5 \times 10^4 \, N$ through a distance of $3 \, m$. Assuming that the resistance due to water is negligible,the speed of the ship is ........... $m/s$.

$A$ block of mass $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. According to observer $B$,the net work done on the block is

$A$ body of mass $6 \,kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4} \,m$, where $t$ is time in seconds. The work done by the force in $2 \,s$ is: (in $\,J$)

$A$ force of $(4\hat i + \hat j + 3\hat k) \, N$ acts on a body,causing its displacement from $(3\hat i + 2\hat j - 6\hat k) \, m$ to $(14\hat i + 13\hat j + 9\hat k) \, m$. Calculate the work done in $J$.

$A$ particle moves from position $\vec{r}_1 = 3\hat{i} + 2\hat{j} - 6\hat{k}$ to position $\vec{r}_2 = 14\hat{i} + 13\hat{j} + 9\hat{k}$ under the action of force $\vec{F} = 4\hat{i} + \hat{j} + 3\hat{k} \text{ N}$. The work done will be ............ $\text{J}$.

$A$ block of mass $2 \,kg$ is pulled at a constant speed with a taut rope along a frictionless plane that is inclined at $30^{\circ}$. Then the work done by the tension in the rope in pulling it a distance $4 \,m$ along the inclined plane in joule is (acceleration due to gravity $= 10 \,ms^{-2}$)