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## Particles Traveling Vertically Upwards: An Introduction to Kinematics

Particle kinematics is the study of the motion of objects in one-, two-, or three-dimensional space. It is a branch of classical mechanics that deals with describing the motion of objects and solving problems related to the motion of particles. When a particle is projected vertically upwards, its motion is called projectile motion and is a very important topic in kinematics. This article will introduce the concept of projectile motion and explain how it works.### What Is Projectile Motion?

Projectile motion is the motion of an object that is projected into the air and then follows a curved path due to the force of gravity. If an object is projected with some initial velocity and no other forces act on it, then its path will be a parabola. This is because the acceleration due to gravity is constant and acts in a downward direction.### Types of Projectiles

There are two types of projectile motion: horizontal and vertical. In horizontal projectile motion, the object is projected at an angle to the horizontal and follows a curved path. In vertical projectile motion, the object is projected vertically upwards and follows a parabolic path.### Equations of Motion

The equations of motion for a particle projected vertically upwards are the same as those for any other type of projectile motion. The equations are expressed as a set of three equations: the equation of motion, the equation of conservation of energy, and the equation of conservation of momentum. The equations of motion for a particle projected vertically upwards are:- The equation of motion: v = v
_{0}+ at, where v is the velocity, v_{0}is the initial velocity, a is the acceleration due to gravity and t is the time. - The equation of conservation of energy: E = mgh, where E is the energy, m is the mass of the particle, g is the acceleration due to gravity, and h is the height of the particle.
- The equation of conservation of momentum: p = mv, where p is the momentum, m is the mass of the particle and v is the velocity.