# Chapter 2 – Motion in one dimension

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

A body is defined as a fixed amount of matter with limited boundaries in all four directions. A body has a fixed shape and occupies a designated space in the space. You might have come across this simple observation that things seem to move when they rest according to other dimensions. In this article, you will get all the information about motion in one dimension.

#### What is a Particle?

A particle refers to a small portion of the surrounding matter and is very small in size. During the study of particles, the distance and dimensions are usually neglected. Therefore, a particle is defined as a fixed part of matter that has a definite position in the space but not a concrete size.

#### What do you mean by Motion in one dimension?

We all have seen in our daily lives that an object’s position can change at any time. Whenever a particle moves in a straight line, its situation changes for the frame’s fixed time.

Therefore, we can define Motion as below:

When an object or a particle changes its position when it travels on a straight line, it can also change its position concerning the origin or any other fixed point of the frame. An object or a particle is also said to be in Motion when it changes its position continuously concerning a fixed point. A body is said to be in Motion if every part of it moves in the same direction at the same speed.

Whenever a particle or a body travels or changes its position on a straight line, it is Motion in one dimension.

#### What is the meaning of the frame of reference?

We all must have seen the railway platform from the running trains. It usually seems like all the things that are placed on the platform are also changing their positions. But if you go and stand on the platform, you will find out that the items placed on the forum are at rest.

Therefore, if a person takes training as the reference frame, the platform’s objects are not stationary. But if the person takes the platform as the reference, the things on the platform are static. In other words, there is a significant need to define a frame of reference in which a person studies the Motion of an object. A frame of reference can also be defined as a set of coordinate axes that are definite concerning a point in the space.

#### Distance

We know that displacement is defined concerning direction but not distance. The magnitude of the displacement is known to be the distance. We have to keep in mind while solving the questions of kinematics that the distance traveled between two points is not exactly the same concept as the distance actually between them. Distance is the absolute path that an object travels between two specific positions. As we know, space has no directions, so it also has no sign.

#### Scalar and vector quantities

A scalar quantity is defined as a quantity that has no direction. A scalar quantity only has magnitude. A vector quantity is defined as a quantity that has both magnitude and direction.

Some examples of scalar quantities are-

• Speed
• Time
• Area
• Mass

Some examples of vector quantities are-

• Acceleration
• Momentum
• Velocity
• Displacement

#### Speed

The speed of a substance is defined as the ratio of distance to the time that it takes to cover the distance. It is a scalar quantity.

Speed=d/t

In this formula,

• s  or speed is measured in m.s-1
• d is the amount of distance measured in m
• t is the time taken by the particle and is measured in s

The four types of speed that we use in motion are:

• Uniform speed
• Average speed
• Instantaneous speed
• Variable speed

#### Velocity

The velocity of an object is defined as the rate of the change of the position of the object wrt the frame of reference. Velocity is a vector quantity. It has both magnitude and direction. The SI unit of velocity is meter per second.

#### Displacement

If an object is seen moving at a relative position wrt to the frame of reference (for instance, if a man is seen moving at a relative position wrt to the frame of reference such as a building), there is a change in the object’s position. This concept of change in the relative position of an object is known as displacement.

Displacement is described as the change that occurs in the position of any object:

Δx = xf − xo,

where Δx is displacement

xf is the final position

x0 is the initial position.

In this, the Δ (delta) is the Greek letter that describes “change in” whichever quantity follows it; So, Δx means to be changed in position. To find displacement, we need to subtract the initial position from the final position of the object.

#### Acceleration

When an object moves in space with constant acceleration, its velocity decreases or increases at a fixed rate throughout its Motion. The concept of average acceleration is equal to the acceleration at any instant keeping the acceleration constant.

Negative acceleration comes up in two cases-

• Case 1: When the object undergoes a decreasing velocity while moving in a positive direction.
• Case 2: When the thing experiences an increasing rate while driving in a negative order.

#### Graphical Representation Of Motion

An acceleration time graph is used to determine the change in the velocity of an object in a fixed interval of time.

A Displacementtime graph is used to show the displacement of a moving object in a given period of time.

A velocity-time graph is used to determine the speed and direction of an object in a given interval of time.

Three Equations of Motion are:

• v = u + at
• s = ut + (1/2) at2
•  v2 = u2 + 2as

#### Conclusion

The displacement is independent of the path taken in traveling between the two positions and is simply the difference in the two marks’ function and is independent of the path taken in traveling between the two characters. The distance is the total path taken between the two positions.

#### FAQs

1. What is the Position Vector?
A position vector has used the position of a particle at any instant. It is a vector notation that joins the origin with the moving particle.
2. What is speed?
Speed is defined as the rate of change of distance per unit of time.
3. What is acceleration?
Acceleration is defined as the rate of change of velocity per unit of time. The use of acceleration comes up in the case of non-uniform motion. It is always a vector quantity.
4. What are scalar and vector quantities?
Scalar quantities only have magnitude. Vector quantities have magnitude as well as direction.
5. What do you mean by kinematics?
Kinematics refers to a branch of physics that deals with the motion of objects without considering their reference to forces.

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• Acids, Bases And Salts
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### Middle School Math

• Area and Its Boundary
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