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 $=10 \mathrm{~ms}^{-2}$ )

The linear momentum of a body of mass 8 kg is $24 \mathrm{~kg} \mathrm{~ms}^{-1}$. If a constant force of 24 N acts on the body in the direction of motion of the body for a time of 3 s , then the increase in the kinetic energy of the body is

A person holds a ball of mass 0.25 kg in his hand and throws it, so that it leaves his hand with a speed of $12 \mathrm{~ms}^{-1}$. In this process, if his hand moved through a distance of 0.9 m , then the net force acted on the ball is

A particle of mass $m$ at rest on a rough horizontal surface with a coefficient of friction $\mu$ is given a

velocity $u$. The average power imparted by friction before it stops