$A$ 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 $, m$)

$(a)$ State Newton's second law of motion and show that the first law of motion can be mathematically derived from the mathematical expression for the second law of motion.
$(b)$ A stone dropped from a window reaches the ground in $0.5 \, s$ (given $g = 10 \, m \, s^{-2}$):
$(i)$ Calculate the speed just before it hits the ground.
$(ii)$ What is the average speed during $0.5 \, s$?
$(iii)$ Calculate the height of the window from the ground.

Why is it advised to tie luggage with a rope on the roof of buses?

It is required to increase the velocity of a scooter of mass $80 \ kg$ from $5 \ m s^{-1}$ to $25 \ m s^{-1}$ in $2 \ s$. Calculate the force required.

Two forces $F_{1} = 20 \, N$ and $F_{2} = 30 \, N$ are acting on an object in opposite directions as shown in the figure.
$(i)$ What is the net force acting on the object?
$(ii)$ What is the direction of the net force acting on the object?
$(iii)$ If the mass of the body is $10 \, kg$,what will be the acceleration produced in it?

$(a)$ Why do we jerk wet clothes before spreading them on a clothesline?
$(b)$ Fruits fall off the branches when a strong wind blows. Give a reason.