**Kinematics: The Geometry of Motion**

Kinematics is a branch of mechanics that describes the motion of points, bodies (objects), and systems of bodies without considering the forces that cause them to move. It focuses on the geometric aspects of motion.

**1. Displacement, Velocity, and Acceleration**

**Displacement**is a vector quantity that represents the change in position of an object. It has both magnitude and direction.**Velocity**is also a vector quantity that describes the rate of change of displacement. It tells us how fast an object is moving and in which direction.**Acceleration**is the rate of change of velocity over time. Like velocity and displacement, acceleration is a vector quantity.

**2. Equations of Motion**

The equations of motion, also known as the kinematic equations, describe the relationship between displacement, velocity, acceleration, and time under uniform acceleration. They are:

- v = u + at
- s = ut + 1/2 at^2
- v^2 = u^2 + 2as

where:

**u**is the initial velocity,**v**is the final velocity,**a**is the acceleration,**s**is the displacement,**t**is the time.

**3. Projectile Motion**

Projectile motion is a form of motion experienced by an object or particle that is thrown near the Earth’s surface and moves along a curved path under the action of gravity only. The key points about projectile motion are:

- The horizontal and vertical motions are independent of each other.
- The only acceleration acting on the projectile is the acceleration due to gravity, which acts downward.