$A$ man who is running has half the kinetic energy of a boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was:

$A$ body starts moving unidirectionally under the influence of a source of constant power. Which one of the graphs correctly shows the variation of displacement $(s)$ with time $(t)$?

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially,$S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision,$S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision:

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

Two identical balls of mass $2 \ kg$ are moving towards each other with a velocity of $5 \ m/s$. They collide and come to rest after the collision. What is the work done by the internal forces in $J$?

$A$ truck and a car are moving with equal velocity. On applying the brakes,both will stop after a certain distance. Which of the following is true?