$A$ body of mass $2 \, kg$ is projected vertically upwards with a kinetic energy of $490 \, J$. At what height will its kinetic energy become half of its initial value? $(g = 9.8 \, m/s^2)$

$A$ force acts on a $3 \,g$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$,where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,s$ is ..... $mJ$.

$A$ ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$,its speed at $A$ must be .......... $m/s$ (Take $g = 10 \,m/s^2$,mass of the body = $5 \,g$).

$A$ block of mass $100 \, g$ moves on a rough surface. The heat produced when its velocity changes from $10 \, m/s$ to $5 \, m/s$ is ....... $J$.

$A$ body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x$ into the sand,the average resistance offered by the sand to the body is

What is the difference between work done on a body by a force and work done by a body?