Theory:

In certain cases, motion is observed indirectly. For example, the movement of dust and leaves on a tree denotes the flow of air from one place to another; the wonderful phenomena of sunrise and sunset show the Earth's rotation, and the change of seasons every year shows the motion of the Earth around the Sun.

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Motion of the Earth around the Sun
 
While travelling on a train, the trees on the sides seem to be moving backwards. Have you ever noticed this? If so, do you think the same will apply to a person standing near the tree?
The answer will be, NO!
 
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Moving trains
  
When we are sitting on a train that is actually at rest, sometimes it appears to move. As motion is relative, if the objects outside the train move, our eyes perceive it in a way that we are moving.
  
Relative phenomenon:
An object can appear to be moving for one person, while it seems to be stationary for another. Hence, motion is a relative phenomenon.
The roadside trees seem to be moving backwards to travellers sitting on a moving bus. Standing on the side of the lane, the other person sees the bus and its passengers moving. In the meanwhile, a passenger onboard notices that his fellow passengers are resting.

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A moving bus
 
Now we know the motions are relative; then let us see the classifications of the motions.
 
S. No
Type of motion
What is it?
Example
1.
Linear motion
The object moves along a straight line.
A car travelling in straight road.
2.
Circular motion
The object travels in a circular path.
Movement of artificial satellite orbiting the earth.
3.
Periodic or oscillatory motion
Objects that are in repeated motion for equal intervals of time.
The pendulum of a clock.
 
Motions are complex sometimes. Objects may move in a straight line or a circle. Sometimes, it may rotate or even vibrate. In certain situations, it can be a combination of all of these.