Laws of Motion: Newton's Principles

An object at rest remains at rest, and an object in motion remains in motion at constant velocity unless acted upon by a net external force.
This law defines inertia, the tendency of objects to resist changes in their state of motion.

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Formula: ( F = ma )
- ( F ) = force (N)
- ( m ) = mass (kg)
- ( a ) = acceleration (m/s²)

Motion in a straight line with constant speed.
Characteristics:
- Equal distances covered in equal intervals of time.
- No acceleration.

Motion with varying speed or direction.
Characteristics:
- Unequal distances covered in equal intervals of time.
- Acceleration may be present.

Change in velocity per unit time.
Formula: ( a = \frac{\Delta v}{\Delta t} )
- ( \Delta v ) = change in velocity (m/s)
- ( \Delta t ) = change in time (s)
Can be positive (speeding up), negative (slowing down), or zero (constant speed).

First Equation of Motion:
- ( v = u + at )
- ( v ) = final velocity
- ( u ) = initial velocity
- ( a ) = acceleration
- ( t ) = time
Second Equation of Motion:
- ( s = ut + \frac{1}{2}at^2 )
- ( s ) = displacement
Third Equation of Motion:
- ( v^2 = u^2 + 2as )

Graphical interpretation involves plotting velocity vs. time to find displacement or acceleration.

Newton's First Law: Objects maintain their state of motion unless influenced by a net external force, illustrating the concept of inertia.

Newton's Second Law: Describes the relationship between force, mass, and acceleration.
- Formula: ( F = ma ) indicates that force increases with greater mass or acceleration.
Newton's Third Law: Establishes that for every force exerted, there is an equal and opposite force reacting back, emphasizing the interaction of forces.

Speed: Measures how fast an object moves; calculated by distance divided by time.
- Formula: ( \text{Speed} = \frac{\text{Distance}}{\text{Time}} )
- Considered a scalar quantity, as it has magnitude only.
Velocity: Considers both speed and direction; reflects how quickly an object changes position.
- Formula: ( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} )
- Classified as a vector quantity due to its directional component.

Distance: Total length of travel made by an object regardless of direction, always a positive value.
Displacement: Measures the shortest straight-line distance between starting and ending points and includes direction.
- Can take positive, negative, or zero values depending on the position change.

Uniform Linear Motion: Occurs when an object moves at constant speed along a straight path; characterized by equal distance covered over equal time intervals, thus no acceleration.
Non-Uniform Linear Motion: Involves changing speed or direction; characterized by unequal distance coverage over equal time intervals, which may involve acceleration.

Acceleration: Describes the rate of change of velocity over time, indicating how quickly an object speeds up or slows down.
- Formula: ( a = \frac{\Delta v}{\Delta t} ) where ( \Delta v ) is the change in velocity and ( \Delta t ) is the change in time.
- Can be positive, negative, or zero, depending on the object's speed behavior.

First Equation of Motion: Relates final velocity to initial velocity, acceleration, and time.
- Formula: ( v = u + at )
Second Equation of Motion: Describes displacement as a function of initial velocity, time, and acceleration.
- Formula: ( s = ut + \frac{1}{2}at^2 )
Third Equation of Motion: Links final velocity, initial velocity, acceleration, and displacement.
- Formula: ( v^2 = u^2 + 2as )
Graphical Representation: Involves plotting velocity versus time graphs to analyze displacement and acceleration visually.