Motion around us - class-XI

According to Newtons's first law , body remains in its state unless acted by external force. This property of body is termed as Inertia.

This totally depends on the frame of refrence, any object is relatively at rest or moving.

Earth is continously moving in its orbit around the sun and on its own axis.

when the position of a body does not change with respect to its surroundings and time the body is said to be in rest. A book lying on the table is at rest because its position with respect to other object on table or room is fix. 

A book lying on the table is at rest. 

Pendulum of a wall clock- It is in periodic motion. Rest all are in multiple motion. The restoring force is proportional to displacement .While electric drill, rolling ball etc are in multiple motion like rotational +transnational or Vibrational motion.

Giant wheel- because it has rotational motion as well as transnational motion. While apple falling from a tree, a car moving on straight rod and coin moving over a carrom board have only linear or rectilinear motion.  

Moon 

Earth, because earth is in motion while other object are in rest with respect to earth.  

All the three object are in any osscilatory motion wrt to earth as frame of refrence. But study table is at rest.

The relation between kinetic energy $(K)$ and momentum $(p)$ is given by, $K=\dfrac{p^2}{2m}$ where $m$ be the mass of the body

Changes with time

Impulse:- It is defined as a change in momentum due to force in small time.

The relative speed of the first train with respect to the second is 30 - 20 = 10 m/s. The total distance to be covered to overtake is the sum of the lengths of both trains: 200 + 300 = 500 m. Time = Distance / Relative Speed = 500 / 10 = 50 s.

when bus suddenly start moving in forward direction. This happens due to. When a bus suddenly starts, the standing passengers fall backward in the bus.

The walls are at rest with respect to the Earth. When you are sitting in the classroom, you are also at rest with respect to the Earth, and so the walls do not seem to be moving to you.

according to newton's first law of motion, an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The maximum height of a projectile is H = (vertical component of velocity)²/(2g). If vector u = aî + bĵ + cĵ with î east, ĵ north (horizontal), and ĵ vertical, then the vertical component of initial velocity is c (assuming cĵ represents the vertical direction, which typically uses the unit vector k̂, but in this notation cĵ or ck̂ would give the vertical component c). Maximum height = c²/(2g).