Motion in a Straight Line

Distance and displacement are different quantities
- Distance is the actual path length travelled
- Displacement is the change in position
Distance is always positive, and cannot decrease with time
Displacement can be positive, negative or zero depending on the direction of motion
For uniform motion in a straight line:
- Displacement = Initial Position Vector - Final Position Vector
- This gives the shortest path length between the two positions

Average velocity = Total displacement / Total time
- Can be calculated by (Initial velocity + Final velocity) / 2
Instantaneous velocity = Rate of change of position with respect to time
- Represented by the slope of the position-time graph

Acceleration is the rate of change of velocity with respect to time
If acceleration is constant:
- Average velocity = (Initial velocity + Final velocity)/2
- Displacement = (Initial velocity + Final velocity)/2 * Time
Instantaneous acceleration is the slope of the velocity-time graph

v = u + at
s = ut + (1/2)at^2
v^2 = u^2 + 2as
Where:
- v = Final velocity
- u = Initial velocity
- a = Acceleration
- s = Displacement
- t = Time### Physics - Uniform and Non-Uniform Motion
The text discusses various concepts related to uniform and non-uniform motion
Key points:
Equations of motion for objects moving with constant acceleration
Calculating displacement, velocity, and time for an object under constant acceleration
Analyzing motion graphs - position-time, velocity-time, acceleration-time
Comparing motion of objects dropped from the same height with different initial velocities
Analyzing motion of an object thrown vertically upwards
Calculating time of flight, maximum height, and velocity on reaching the ground
Relationship between time taken for equal distance intervals in uniform and non-uniform motion
Analyzing relative motion of two objects moving in opposite directions

The text emphasizes the importance of thoroughly understanding core concepts
Recommends actively practicing solving various types of problems
Highlights common exam question formats and strategies to approach them
Advises recalling and applying relevant formulas and relationships### Uniform Circular Motion and Non-Uniform Circular Motion
Uniform circular motion is a type of motion where the object moves in a circular path with a constant angular velocity
In uniform circular motion:
- Angular velocity (ω) is constant
- Linear speed (v) is proportional to the radius (r)
- Acceleration has two components:
  - Tangential acceleration (a_t) which is zero, since speed is constant
  - Centripetal acceleration (a_c) which is directed towards the center and has a magnitude of v^2/r
Non-uniform circular motion is when the object's speed changes during the circular motion
In non-uniform circular motion:
- Angular velocity (ω) can change
- Linear speed (v) can change
- Acceleration has two components:
  - Tangential acceleration (a_t) which causes changes in speed
  - Centripetal acceleration (a_c) which causes changes in direction

Relative velocity between two objects is the vector difference between their individual velocities
For a collision to occur, the relative velocity between the objects must be opposite to their relative position vector
The condition for minimum distance between two objects during collision is d/√2, where d is the initial distance between them

Distance is the actual path length travelled, whereas displacement is the change in position.
Distance is always positive and cannot decrease with time.
Displacement can be positive, negative, or zero, depending on the direction of motion.
For uniform motion in a straight line, displacement is calculated as the initial position vector minus the final position vector, giving the shortest path length between the two positions.

Average velocity is the total displacement divided by the total time and can be calculated using the formula (initial velocity + final velocity) / 2.
Instantaneous velocity is the rate of change of position with respect to time and is represented by the slope of the position-time graph.

Acceleration is the rate of change of velocity with respect to time.
If acceleration is constant, then the average velocity can be calculated as (initial velocity + final velocity) / 2.
Displacement can be calculated as (initial velocity + final velocity) / 2 * time if acceleration is constant.
Instantaneous acceleration is the slope of the velocity-time graph.

v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

Equations of motion can be used to describe objects moving with constant acceleration.
Displacement, velocity, and time can be calculated for an object under constant acceleration.
Motion graphs, such as position-time, velocity-time, and acceleration-time graphs, can be analyzed.
The motion of objects dropped from the same height with different initial velocities can be compared.
The motion of an object thrown vertically upwards can be analyzed, including calculating time of flight, maximum height, and velocity on reaching the ground.
The relationship between time taken for equal distance intervals in uniform and non-uniform motion can be analyzed.
The relative motion of two objects moving in opposite directions can be analyzed.

When solving physics problems, it is essential to identify the given information and the equations to use.
Values should be substituted into the equations and solved algebraically.
Units should be checked, and dimensional analysis should be performed.
Trends and patterns in the solution should be analyzed.
Complex problems should be broken down into simpler steps.

Uniform circular motion occurs when an object moves in a circular path with a constant angular velocity.
In uniform circular motion, the angular velocity (ω) is constant, and the linear speed (v) is proportional to the radius (r).
The acceleration in uniform circular motion has two components: tangential acceleration (a_t) and centripetal acceleration (a_c).
Non-uniform circular motion occurs when the object's speed changes during the circular motion.
In non-uniform circular motion, the angular velocity (ω) can change, and the linear speed (v) can change.
The acceleration in non-uniform circular motion has two components: tangential acceleration (a_t) and centripetal acceleration (a_c).

The relative velocity between two objects is the vector difference between their individual velocities.
For a collision to occur, the relative velocity between the objects must be opposite to their relative position vector.
The condition for minimum distance between two objects is that their relative velocity must be zero.