# Chapter 4 – Motion in a Plane

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

Introduction

Motion in a Plane as Referred to Motion in Two Dimensions

Motion in a plane can be better understood by motion in two dimensions, as dimensions construct a plane. Our regular motion is in three-dimensional but to understand it you need to know Motion in two dimensions. We will explain this chapter by taking into consideration two axes, one is X-axis, and the other is Y-axis. You have to know about motion in one dimension to derive the equations of Relative Motion and Projectile Motion.

#### Motion in a plane

First, you have to learn the motion equations in a straight line to get a clear idea of equations of motion in a plane. The equations of motion in a straight line are:

• v= u+at
s=ut +½ at2
v2=u2+2as

Here,

• ‘v’ refers to the particle’s final velocity
• ‘u’ refers to the particle’s initial velocity
• ‘S’ refers to the particle’s displacement
• ‘a’ refers to the particle’s acceleration
• ‘t’ refers to the particle’s consideration in the time interval

This same equation has to be put separately in both X-axis and Y-axis in a Plane.

Now, we will get the equation of motion in a Plane from the above equation:

• Vy= uy + ayt
Sy=uyt+ ½ ayt2
V2y =u2y+ 2ays

Here,

• ‘vy’ refers to the particle’s final velocity in the ‘y’ direction
• ‘uy’ refers to the particle’s initial velocity in the ‘y’ direction
• ‘sy’ refers to the particle’s displacement in the ‘y’ direction
• ‘ay ‘refers to a particle’s acceleration in the ‘y’ direction
• ‘t’ refers to a time interval where the particle is in consideration

Likewise, for X-axis :

• Vx= ux + axt
Sx=uxt+ ½ axt2
V2x =u2x+ 2axs

Here,

• ‘vx’ refers to the particle’s final velocity in the ‘x’ direction
• ‘ux’ refers to the particle’s initial velocity in the ‘x’ direction
• ‘sx’ refers to the particle’s displacement in the ‘x’ direction
• ‘ax ‘refers to the particle’s acceleration in the ‘x’ direction
• ‘t’ refers to a time interval where the particle is in consideration

Some topics will help you to understand the topic’ Motion in a Plane’ better. These topics are briefly discussed below:-

• Scalars and Vectors: Scalars and Vectors are physical quantities. The direction of Scalar and Vector quantities are different. The quantity of Scalars has magnitude, and Vectors have both a direction and magnitude. When you learn about motion in a plane, you must know about the characteristics of Vectors and Scalar Quantities.
• Addition and Subtraction of Vectors Graphical Method: Vector is a physical quantity that has magnitude and a direction. The direction of vectors can be explained graphically by addition and subtraction signs.
• Relative
Velocity in Two Dimensions: It means a particle’s acceleration is the same by measuring two observers moving at a constant relative velocity to each other.
• Uniform Circular Motion: When the circular motion that a particle executes has a constant speed, and the circle is always at a fixed radius, then it is known as Uniform Circular Motion.
• Centripetal Acceleration: When the property of the motion of a body traversing a circular path is known as Centripetal Acceleration.

#### What is Relative Motion?

By saying the motion of body P relative to Q, we understand that P’s motion, as perceived from Q’s frame of reference. We can mathematically represent it as:

VQP=VQ-VP

Here,

• ‘VQP’ refers to Q’s velocity as perceived from P
• ‘VQ’ refers to ‘Q’s velocity from the earth like the reference frame
• ‘VP’ refers to ‘P’s velocity from the earth like the reference frame

#### What is Projectile Motion?

A projectile is an object, and here gravity is the only force. One of the most common examples of motion in a Plane is Projectile Motion. In the case of projectile motion, the acceleration acts only in the vertical direction, and this acceleration is because of gravity (g). Hence, to determine the unknown parameters, we can apply equations of motion separately on X-axis and Y-axis.

#### FAQs for Motion in a Plane

What is the motion of a projectile?

Ans: Projectile motion is a kind of motion where the particle or an object is projected near Earth’s surface and moves in a curved way about the action of gravity only.

What are the 2 types of projectile motion?

Ans: The 2 types of projectile motions are horizontal motion (X-axis) and vertical motion (Y-axis).

The X-axis is responsible for the particle’s horizontal and forward motion and uniform velocity.

The Y-axis is responsible for the particle’s vertical and downward motion and uniform acceleration.

What is the velocity of a plane?

Ans: The velocity of a plane regarding the ground is the same as the velocity of a plane regarding the air’s velocity and the velocity of the air regarding the ground.

What is motion class 11?

Ans: When the position of a particle changes regarding its surroundings, it is called motion.

The term motion in a plane is referred to as the motion in two dimensions. One is horizontal dimensions, and the other is the vertical dimension.

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### High School Math

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

• Area and Its Boundary
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