$A$ box '$A$' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time '$t$',it decelerates. Then the reaction $R$ by the floor on the box is given best by

On which factors does the stopping distance of a vehicle depend?

$A$ cold soft drink is kept on a balance. When the cap is opened,the weight reading on the balance:

$A$ man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground,and between the block and the ground.

$A$ pebble of mass $0.05 \, kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,$(a)$ during its upward motion,$(b)$ during its downward motion,$(c)$ at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance.

Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.