$A$ particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec{F} = (3\hat{i} + 4\hat{j})$ through two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then

$A$ 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?

$A$ force of $5 \, N$ acts on a $15 \, kg$ body initially at rest. The work done by the force during the first second of motion of the body is

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

$A$ ball of mass $m$ is attached to a string whose other end is fixed. The system is free to rotate in a vertical plane. When the ball swings,no work is done on the ball by the tension in the string. Which of the following statements is the correct explanation?

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