$A$ body of mass $m$ accelerates uniformly from rest to a speed $v_0$ in time $t_0$. The work done on the body till any time $t$ is

$A$ force $\overrightarrow F = (5\hat i + 4\hat j) \ N$ acts on a body and produces a displacement $\overrightarrow S = (6\hat i - 5\hat j + 3\hat k) \ m$. The work done will be $J$.

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

$A$ string is used to pull a block of mass $m$ vertically up by a distance $h$ at a constant acceleration $\frac{g}{3}$. The work done by the tension in the string is ..............

$A$ body constrained to move along the $z$-axis of a coordinate system is subject to a constant force $F$ given by $F = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$,where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the $x, y,$ and $z$-axes of the system respectively. What is the work done (in $J$) by this force in moving the body a distance of $4 \text{ m}$ along the $z$-axis?

$A$ 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 ........... $m/s$.