This document discusses rectilinear motion of particles. Rectilinear motion refers to motion along a straight line, with position defined by the distance x from a fixed origin O. Velocity is defined as the rate of change of position with respect to time. Acceleration is defined as the rate of change of velocity with respect to time. Displacement refers to the change in position, while distance traveled is the total length of the path traveled over a time interval. The document provides mathematical definitions and derivations for these key concepts in rectilinear motion.

1. Contents
RECTILINEAR MOTION OF PARTICLE :
1. Kinematics of a Particle
2. Rectilinear Motion
Velocity / Acceleration / Displacement /
Distance Traveled
3. Types of Applications
EQUATION OF MOTION

2. RECTILINEAR MOTION OF PARTICLE
◆ Rectilinear Motion
 In rectilinear motion, the particle moves along a straight line,
which is considered to be the x axis.
 The kinematics of the motion is described as follows:
The position of the particle is defined by the distance x between the
particle and a fixed origin O on the straight line. The position x varies
with the time during the motion, i.e.,
Where
is a certain function of the time .

3. RECTILINEAR MOTION OF PARTICLE
1. The velocity(V)
The instantaneous velocity of the particle ( its velocity at any
instant ) is defined by the rate of change of its position with respect
to the time, i.e.,

4. RECTILINEAR MOTION OF PARTICLE
2. The Acceleration (a)
It is defined as the time rate of change of the particle`s velocity, i.e.,
In some cases, as we will see later, it will be necessary to substitute
the acceleration in the following mathematical form:
Which is derived as follows:

5. RECTILINEAR MOTION OF PARTICLE
3. The displacement (x)

6. RECTILINEAR MOTION OF PARTICLE
4. The Distance travelled (D)
The distance travelled during a time interval is defined by the total
length of the path over which the particle travels.

7. RECTILINEAR MOTION OF PARTICLE
4. The Distance travelled (D)
The distance travelled during a time interval is defined by the total
length of the path over which the particle travels.