Rectilenear motion of particles

Motion is the change in the position of a body. To explain it further, if the coordinates of the position of a body change concerning a reference point over time, then physics dictates that the body is in motion. Motion can be of many types, and the patterns in which these coordinates change over time determine the type of motion. The common among them include:

Projectile Motion: When the body's motion is in two dimensions (vertical and horizontal), then it is known as projectile motion. Any object thrown in space is an example of projectile motion until you throw it vertically upwards or downwards.
Linear Motion: When a body makes any motion in only one direction and in a linear pattern such that there is a change of coordinates of only one axis, this motion is an example of linear motion.
Circular Motion: When the motion of a body is periodic or along a defined circle, it is a form of circular motion.

How to define the Rectilinear Motion of Particles?

Rectilinear motion is the same as the linear motion of particles. When there is a change in the coordinates of a single axis, then the motion is rectilinear.
It is of three types:

Uniform Rectilinear Motion: The rectilinear motion of the body without any acceleration (constant speed) is uniform rectilinear motion.
Rectilinear Motion with Non-Uniform Acceleration: The motion of a body in a straight line with non-uniform acceleration is rectilinear motion with non-uniform acceleration. The force acting on the body is not constant.
Rectilinear Motion with Uniform Acceleration: In this type of motion, the body undergoes motion with constant acceleration (the speed increases with a constant factor). The force acting on the body is constant.

Some Terms Associated with Rectilinear Motion

Distance and Displacement

Distance is the total length covered by the body during its course of motion. The unit of distance is metres and has dimensions [L].

Displacement is the shortest possible length between the initial position and the final position. Displacement is also measured in metres and has the dimension [L]. The only thing different in displacement from a distance is that it is a vector quantity and has a direction of motion.

Speed and Velocity

Speed is the measure of the length covered by the body in unit time. It is the distance covered in the unit time interval. The unit is metres/second, and it is a scalar quantity. The dimensions are [L][T-1].

Velocity is the measure of the displacement of the body in unit time. It is similar to speed in units of measurement and dimensions, but it is a vector quantity and has a direction along with magnitude, unlike speed.

Speed = Distance/Time

Velocity = Displacement/Time

Acceleration

Acceleration is the second derivative. It is the velocity change rate. It is measured in metres/second2 and the dimension is [L][T-2].

Formulas for Rectilinear Motion

v= u+ at
s= ut+ ½ at2
v2=u2 + 2as

Where,
s is the distance travelled under acceleration
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time for which acceleration takes place

The examples of rectilinear motion include:

Planes fly in a rectilinear motion.
Elevators move in a rectilinear motion.
Freefall is an example of rectilinear motion.
The army movement in the form of the parade is a rectilinear motion.

Difference of Rectilinear Motion and Linear Motion

Rectilinear Motion	Linear Motion
The rectilinear motion requires at least two bodies moving parallel to each other in a straight line.	Linear motion is a motion when the coordinates of a body change in just one axis.
The rectilinear motion contains the aspect of acceleration.	Linear motion can only be uniform linear motion and non-uniform linear motion.