# Rectilinear Motion of Particles

Motion is one of the most common phenomena we come across in our daily lives. For example, a moving car, a kid running on the road or a fly moving in the air are all said to be in motion. So, in general terms, a body is said to be in motion if it changes its position with respect to a reference point and time. Depending upon the path taken by the particle the motion can be of different types like projectile motion, rectilinear motion, rotational motion, etc. For now, we will only focus on the rectilinear motion which is also known as linear motion.

## What is Rectilinear Motion?

When we require only one co-ordinate axis along with time to describe the motion of a particle it is said to be in linear motion or rectilinear motion. Some examples of linear motion are a parade of soldiers, a train moving along a straight line, and many more.

### Distance and Displacement

So now that we have learned about linear motion we will discuss two terms related to change in position. These are called – ‘Distance’ and ‘Displacement’.

Distance is defined as,

The total path length covered during a journey

While displacement is defined as,

The path length from final position of the particle to the origin O.

Consider the following figure:

We have an origin O, measurements to the right of O are taken as a positive while to the left are taken as negative. Suppose a person who starts from origin O reaches point A,

Distance = OA

Displacement = OA

Now he turns and reaches point B,

Distance = OA + AB

Displacement = -OB

As we can see, displacement is negative since it is measured to the left of the origin. From the above example, we can infer that distance is always positive while displacement can either be positive or negative.

### Speed and Velocity

These terms are used to describe the rate of change of position. Speed is the rate of change of distance while velocity is the rate of change of displacement. Comparing from above as distance can never be negative so the speed is never negative while velocity can be both positive and negative. In mathematical terms, these are defined as follows:

Speed = $\frac{Distance~ Travelled}{Time ~Taken}$

Velocity =$\frac{(Final~ position – Initial~ position)}{Time~ Taken}$

## Examples for Rectilinear Motion

Following are the rectilinear motion examples:

• The use of elevators in public places is an example of rectilinear motion.
• Gravitational forces acting on objects resulting in free fall is an example of rectilinear motion.
• Kids sliding down from a slide is a rectilinear motion.
• The motion of planes in the sky is a rectilinear motion.

## Types of Rectilinear Motion

There are three types of rectilinear motion and they are:

• Uniform rectilinear motion: When an object travels at a constant speed with zero acceleration it is known as uniform rectilinear motion.
• Uniformly accelerated rectilinear motion: When an object travels with constant acceleration it is known as uniformly accelerated rectilinear motion.
• Rectilinear movement with non-uniform acceleration: When an object travels at an irregular speed and acceleration it is known as a rectilinear movement with non-uniform acceleration.

### What is the difference between linear and rectilinear motion?

 Linear motion Rectilinear motion An object is said to be in a linear motion when the object moves in a straight line An object is said to be in a rectilinear motion when two objects are moving in a straight line and are parallel to each other There are two types of linear motion, and they are uniform motion and non- uniform motion There are three types of rectilinear motion, and they are uniform rectilinear motion, uniformly accelerated rectilinear motion and rectilinear movement with non-uniform acceleration Athlete running 200 m along the straight track Elevator movement is an example of rectilinear motion

1. 2) How does the velocity change with time in uniform rectilinear motion of an object?
3) A body is moving with a velocity of 10 m/s. if the motion is uniform what will be the velocity
after 10 s?
4) Can a body have constant speed but variable velocity?
5) Differentiate between uniform and non-uniform velocity.
6) Express average velocity when the velocity of the body changes at a uniform and a non-
uniform rate.
7) An object travels along a circular path of radius 70 m. After travelling half a revolution in 20s,
find the average speed and average velocity of the object.

1. 2) When the object changes its direction, the velocity changes.
3) Uniform velocity implies zero acceleration. Hence, v = u + at becomes v = u. The velocity of the body at 10 seconds will be the same as the velocity of the body at 0 seconds, in this case, it will be 10 m/s.
4) Yes, the body can have a constant speed and variable velocity. Whenever the direction changes, the velocity changes.
5) A body is said to have uniform velocity when it covers equal distances in equal intervals of time. A body is said to have non-uniform velocity when it covers unequal distances in equal intervals of time.
6) When the velocity of a body changes at a uniform rate then the average velocity is the mean of initial velocity & final velocity for a specific period of time. Mathematically, it is written as follows:
Average Velocity = (Initial Velocity + Final velocity)/2
When the velocity of a body changes at a non-uniform rate then its average velocity is net displacement covered by the total time taken and is given as,
Average Velocity = Net Displacement/ Total Time Taken
7) The average velocity is calculated as follows:
Average Velocity = Net Displacement/ Time
Average Velocity = (70+70)/20 = 7 m/s
The average speed is calculated as follows:
Average Speed = Total Distance/ Total Time
πr/20 = 220/20 (220 is the approximated value)
=11 m/s

2. Express average velocity when the velocity of a body changes at a non – uniform rate and a
uniform rate.