$A$ man weighing $60 \ kg$ runs along the rails with a velocity of $18 \ km \ h^{-1}$ and jumps into a car of mass $1$ quintal $(100 \ kg)$ standing on the rails. Calculate the velocity with which the car will start travelling along the rails. (in $m \ s^{-1}$)

$(a)$ State the law of conservation of momentum.
$(b)$ $A$ body of mass $2 \, kg$,initially moving with a velocity of $10 \, m s^{-1}$,collides with another body of mass $5 \, kg$ at rest. After the collision,the velocity of the first body becomes $1 \, m s^{-1}$. Find the velocity of the second body.

$(a)$ If the mass of a body is doubled, what happens to its acceleration when acted upon by the same force? Justify your answer.
$(b)$ It is easier to stop a tennis ball than a cricket ball moving with the same speed. Why?
$(c)$ A girl of mass $40 \, kg$ jumps with a horizontal velocity of $5 \, m s^{-1}$ onto a stationary cart with frictionless wheels. The mass of the cart is $10 \, kg$. Find her velocity as the cart starts moving. Assume that there is no external unbalanced force working in the horizontal direction.

$A$ body of mass $500 \, g$ is at rest on a frictionless surface. Calculate the distance travelled by it in $10 \, s$ when acted upon by a force of $10^{-2} \, N$. (in $, m$)

$(a)$ $(i)$ Define momentum. State its $SI$ unit.
$(ii)$ An object of mass $50 \ kg$ is accelerated uniformly from a velocity of $4 \ m/s$ to $8 \ m/s$ in $8 \ s$. Find the magnitude of the force exerted on the object.
$(b)$ State Newton's first law of motion.

The branch of Physics which deals with the motion of objects while taking into consideration the cause of motion is