$A$ particle of mass $1\,kg$ is moving along the $x-$axis,where its velocity depends on the $x-$coordinate as $v = 2\sqrt{x}\,m/s$. Find the net force acting on the particle $2\,s$ after the start of motion.

The displacement $(x)$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$. Choose the incorrect statements from the following.

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion? (in $cm$)

$A$ body starts from rest with an acceleration of $8\,m/s^2$. What distance will it cover in the $5^{th}$ second?

If the engine of a long train moving with constant acceleration crosses a tree with velocity $u$ and the last compartment of the train crosses the same tree with velocity $v$,then the velocity with which the middle compartment crosses the same tree is