Physics - Forces and Motion (Kinematics and Newton's Laws)

Kinematics is the study of motion without considering its causes, focusing on parameters like displacement ($s$), velocity ($v$), and acceleration ($a$).

Scalars are quantities with magnitude only (e.g., distance, speed), whereas Vectors have both magnitude and direction (e.g., displacement, velocity, force).

Instantaneous velocity is the velocity at a specific moment in time, defined as the derivative of displacement with respect to time: $v = \frac{ds}{dt}$.

Acceleration is the rate of change of velocity over time: $a = \frac{\Delta v}{\Delta t}$.

Newton's First Law (Inertia): An object will remain at rest or move with constant velocity unless acted upon by a non-zero resultant force ($F_{net} = 0$).

Newton's Second Law: The resultant force acting on an object is equal to the rate of change of momentum, commonly expressed as $F = ma$ when mass is constant.

Newton's Third Law: If body A exerts a force on body B, body B exerts a force of equal magnitude and opposite direction on body A ($F_{AB} = -F_{BA}$).

Weight ($W$) is the force of gravity acting on an object: $W = mg$, where $g \approx 9.81 \text{ m/s}^2$ on Earth.