$A$ body of mass $3 \text{ kg}$ is moving under the action of a force which causes a displacement of $\left(\frac{t^3}{3}\right) \text{ m}$, where '$t$' is time in seconds. The work done by the force in the first $2 \text{ seconds}$ is: (in $\text{ J}$)

$A$ toy gun fires a plastic pellet with a mass of $0.5\ g$. The pellet is propelled by a spring with a spring constant of $1.25\ N/cm$, which is compressed $2.0\ cm$ before firing. The plastic pellet travels horizontally $10\ cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\ N$. What is the speed (in $SI\ units$) of the bullet as it emerges from the barrel?

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest,the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given,moment of inertia of sphere $= \frac{2}{5} mr^2$].

$A$ sphere is suspended by a thread of length $\ell$. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension point?

$A$ train engine of mass $m$ starts moving such that its velocity varies as $v = k\sqrt{s}$,where $k$ is a constant and $s$ is the distance covered. What is the total work done by all the forces acting on the engine in the first $t$ seconds?

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the net work done on the block is