$A$ body is projected vertically upwards with an initial velocity of $7 \, m/s$. At what height will its kinetic energy become half of its initial value (in $, m$)?

$A$ ball of mass $0.4 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.5 \ m$ while applying the force and the ball goes up to $5 \ m$ height further,find the magnitude of the force (in $N$) $(g = 10 \ m/s^2)$.

$A$ ball of mass $1 \ kg$ moves in a straight line with velocity $v = c x^\alpha$,where $c = 1$ ($SI$ unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x = 0$ to $x = 4 \ m$ is $128 \ J$,then the value of $\alpha$ is

What is the work done on an object moving with a constant speed?

$A$ 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?

$A$ body of mass $1 \ kg$ is under a force, which causes a displacement given by $x = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first second (in $J$).