Page 1: Core Concept of Rest & Motion
Core Concept
Rest and Motion are not absolute; they depend entirely on the OBSERVER's frame of reference.
● If position changes with time -> MOTION
● If position does not change with time -> REST
Classroom Example (Golu & Train)
● For a co-passenger: Golu is at REST (because both are sitting together inside the train).
● For a person standing on the platform: Both Golu and the train are in MOTION because their position is changing
with time.
Important Definitions
1. Rest: When the position of a body does not change with time with respect to the observer.
2. Motion: When the position of a body changes with time with respect to the observer.
★ KEY TAKEAWAY
"Motion and rest are relative terms. If the observer changes, the state changes!"
Page 2: Distance, Displacement, Speed, Velocity &
Acceleration
1. Distance vs Displacement
, Distance Displacement
Actual path covered by the object. Shortest path from initial to final position.
Scalar quantity (magnitude only). Vector quantity (magnitude + direction).
2. Speed & Velocity
● Speed: Distance / Time (Scalar)
● Velocity: Displacement / Time (Vector)
○ Instantaneous: In small time interval dt -> dx / dt
○ Average: Over a large time interval -> Total Path / Total Time
3. Acceleration
● Formula: a = dv/dt (Rate of change of velocity)
● v and a in SAME direction: Speed increases (Acceleration)
● v and a in OPPOSITE direction: Speed decreases (Braking / Retardation)
Page 3: Circular Arc Motion & Average Speed Shortcuts
1. Circular Arc Motion
● Radius = r, Center angle = θ (in Radians)
● Distance: Distance = r × θ (radians)
● Displacement: Displacement = 2r × sin(θ/2)
2. Average Speed Shortcuts
● Case A: Equal Time Intervals (t1 = t2)
When a body travels at different speeds for equal intervals of time:
v_avg = (v1 + v2) / 2
Core Concept
Rest and Motion are not absolute; they depend entirely on the OBSERVER's frame of reference.
● If position changes with time -> MOTION
● If position does not change with time -> REST
Classroom Example (Golu & Train)
● For a co-passenger: Golu is at REST (because both are sitting together inside the train).
● For a person standing on the platform: Both Golu and the train are in MOTION because their position is changing
with time.
Important Definitions
1. Rest: When the position of a body does not change with time with respect to the observer.
2. Motion: When the position of a body changes with time with respect to the observer.
★ KEY TAKEAWAY
"Motion and rest are relative terms. If the observer changes, the state changes!"
Page 2: Distance, Displacement, Speed, Velocity &
Acceleration
1. Distance vs Displacement
, Distance Displacement
Actual path covered by the object. Shortest path from initial to final position.
Scalar quantity (magnitude only). Vector quantity (magnitude + direction).
2. Speed & Velocity
● Speed: Distance / Time (Scalar)
● Velocity: Displacement / Time (Vector)
○ Instantaneous: In small time interval dt -> dx / dt
○ Average: Over a large time interval -> Total Path / Total Time
3. Acceleration
● Formula: a = dv/dt (Rate of change of velocity)
● v and a in SAME direction: Speed increases (Acceleration)
● v and a in OPPOSITE direction: Speed decreases (Braking / Retardation)
Page 3: Circular Arc Motion & Average Speed Shortcuts
1. Circular Arc Motion
● Radius = r, Center angle = θ (in Radians)
● Distance: Distance = r × θ (radians)
● Displacement: Displacement = 2r × sin(θ/2)
2. Average Speed Shortcuts
● Case A: Equal Time Intervals (t1 = t2)
When a body travels at different speeds for equal intervals of time:
v_avg = (v1 + v2) / 2
