$A$ body of mass $5\, kg$ is placed at the origin and can move only on the $x$-axis. $A$ force of $10\, N$ is acting on it in a direction making an angle of $60^\circ$ with the $x$-axis and displaces it along the $x$-axis by $4\, m$. The work done by the force is $...\, J$.

$A$ body of mass $2 \ kg$ is moving along the $x$-direction such that its displacement as a function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma \ m$, where $\alpha = 1 \ m/s^2$, $\beta = 1 \ m/s$, and $\gamma = 1 \ m$. The work done on the body during the time interval $t = 2 \ s$ to $t = 3 \ s$ is . . . . . . $J$.

$A$ 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 $= 10 \,ms^{-2}$)

Given that a force $\vec{F}$ acts on a body for time $t_1$ and displaces the body by $\vec{d}$. In which of the following cases must the velocity of the body increase?

$A$ force acts on a $30 \,g$ particle in such a way that the position of the particle as a function of time is given by $x = \alpha t^2$, where $x$ is in metre, $t$ is in seconds and $\alpha = 1 \,m/s^2$. The work done during the first $4 \,s$ is (in $J$)

If a constant force of $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \text{ N}$ acting on a body of mass $5 \text{ kg}$ displaces it from $(3 \hat{i} - 4 \hat{k}) \text{ m}$ to $(2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m}$, then the work done by the force on the body is (in $\text{ J}$)