## Introduction

In this paper, we investigate the motion of a particle that starts at time t 0 and moves on a number line so that its position at time t is given by xt = t3 − 3t. The objective is to find the velocity and acceleration of the particle at time t = 2 .

### What is a particle?

In physics, a particle is a small localized object to which can be ascribed several physical properties such as mass, position, velocity, and momentum. A common example of a particle is a grain of sand.

### What is a number line?

A number line is a straight line on which every point corresponds to a real number. The numbers can be Positive or Negative integers, or Real numbers. The point corresponding to 0 is called the origin. The numbers on the number line are used to represent quantities such as distances and weights.

## The Position of a Particle

### What is the position of a particle?

At any given time, the position of a particle can be represented by a point on a number line. The position of a particle at time t0 is given by the coordinates (t0, x0), where x0 is the initial position of the particle. The position of a particle at time t is given by the coordinates (t, x), where x is the position of the particle at time t.

### How is the position of a particle determined?

There are three ways to determine the position of a particle: initial position, velocity, and acceleration.

Initial position is the position of the particle at time t0. Velocity is the rate of change of position with respect to time. Acceleration is the rate of change of velocity with respect to time.

## The Motion of a Particle

A particle starts at time t_0 and moves on a number line so that its position at time t is given by:

### What is the motion of a particle?

A particle is an object with mass that is free to move in a three-dimensional space. It can be either a point-like object or a extended object. A particle’s motion is described by its position, velocity, and acceleration. The position of a particle is a vector quantity that indicates the coordinates of the particle in space. The velocity of a particle is a vector quantity that indicates the rate of change of the position of the particle. The acceleration of a particle is a vector quantity that indicates the rate of change of the velocity of the particle.

### How is the motion of a particle determined?

The motion of a particle is determined by its position at any given time. The position of a particle can be represented by a number on a number line. The position of the particle at time t0 is represented by the number 0 on the number line. The position of the particle at time t is represented by the number 1 on the number line.

## Conclusion

In conclusion, the position of a particle at any given time can be determined by its position at time t0 and its velocity.