Chapter 4 – 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.