A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

A body is projected at an angle of $60^{\circ}$ with the horizontal. If the initial kinetic energy of the body is $X$, then its kinetic energy at the highest point is

The bob of a simple pendulum of length 200 cm is released from horizontal position. If $10 \%$ of its initial energy is lost due to air resistance, then the speed of bob at the mean position is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The power required for an engine to maintain a constant speed of $50 \mathrm{~ms}^{-1}$ for a train of mass $3 \times 10^6 \mathrm{~kg}$ on rough rails is

(The coefficient of kinetic friction between the rails and wheels of the train is 0.05 and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )