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

Two constant forces ${F_1} = 2\hat i - 3\hat j + 3\hat k$ $(N)$ and ${F_2} = \hat i + \hat j - 2\hat k$ $(N)$ act on a body and displace it from the position ${r_1} = \hat i + 2\hat j - 2\hat k$ $(m)$ to the position ${r_2} = 7\hat i + 10\hat j + 5\hat k$ $(m)$. What is the work done in $J$?

What is required for work to be done when a force is applied to an object?

An adult weighing $600 \, N$ raises the centre of gravity of his body by $0.25 \, m$ while taking each step of $1 \, m$ length in jogging. If he jogs for $6 \, km$,calculate the energy utilised by him in jogging assuming that there is no energy loss due to friction of ground and air. Assuming that the body of the adult is capable of converting $10 \, \%$ of energy intake in the form of food,calculate the energy equivalents of food that would be required to compensate for the energy utilised for jogging.

$A$ force $\vec F = 5\hat i + 6\hat j - 4\hat k$ acting on a body produces a displacement $\vec s = 6\hat i + 5\hat k$. The work done by the force is $......$ units.

$A$ force of $(-\,1, \,2, \,3) \,N$ is applied to an object,causing a displacement of $4 \,m$ along the $X$-axis. Calculate the work done by the force on the object. (in $,J$)