The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be ............. $Joule$.

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

Statement $(I)$: The slope of the kinetic energy-displacement curve of a body in motion is directly proportional to its acceleration.
Statement $(II)$: From a height of $15 \ m$,a ball is projected vertically upwards with a velocity of $30 \ m/s$. If the ball rises to the same height after hitting the ground,the loss of its energy on hitting the ground is $30 \%$.
Statement $(III)$: The velocity acquired by a body of mass '$m$' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass '$m$'.
Which of the following is correct?

$A$ ball is released from the top of a tower. The ratio of work done by the force of gravity in the first,second,and third second of the motion of the ball is:

$A$ rigid body of mass $4 \ kg$ initially at rest moves under the action of an applied horizontal force of $18 \ N$ on a table with a coefficient of kinetic friction of $0.2$. The work done by the applied force on the body in $10 \ s$ will be $.... \ J$.