# Motion in a Plane: Scalar Quantities, and Vector Quantities (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Motion in a Plane

- The Physical Quantities like Work, Temperature and Distance Can Be Represented in Day-to-Day Life Wholly by Their Magnitude Alone.
- Though, Relation of These Physical Quantities Can Be Explained by the Laws of Arithmetic.
- To Represent Physical Quantities like Acceleration, Displacement, and Force, the Direction is Equally Essential Along with the Magnitude.

## What is Motion in a Plane?

- Motion in a Plane is the Motion in Dimensions, for Instance, Projectile Motion, and Circular Motion and So on.
- Reference to Analyze a Dimensional Motion Will Be the Origin with Two Coordinate Axes i.e.. , and .

The Equations of Motion in a Straight Line Are:

Where,

- V = Final Velocity of the Particle
- U = Initial Velocity of the Particle
- S = Displacement of the Particle
- A = Acceleration of the Particle
- T = Time Interval in Which the Particle is in Consideration

## Scalar Quantities

- Scalar Quantities Are Those Physical Qualities That Can Be Specified Completely by Their Magnitude Alone.
- In Physics It is One That Can Be Described by a Single Element of a Number Field Such as a Real Number, Often Accompanied by Units of Measurement.
- The Examples of Scalar Quantities Are Mass, Density, Temperature, Length, Work, Speed, Etc.
- A Scalar is Usually Said to Be a Physical Quantity That Only Has Magnitude, Possibly a Sign, and No Other Characteristics

## Vector Quantities

- Vector Quantities Are Specified by Both Magnitude and Direction.
- The Examples of Vector Quantities Are Displacement, Acceleration, Momentum, Velocity, Torque, Force, Etc.
- It Refers to the Physical Quantities Characterized by the Presence of Both Magnitude as Well as Direction.
- The Direction of Any Vector Quantity is Specified by a Unit Vector. Vectors Lying in the Same or Parallel to the Same Plane Are Called Coplanar Vectors.

### Difference between Scalar and Vector

Vector | Scalar | |

Definition | A physical quantity with both the magnitude and direction. | A physical quantity with only magnitude. |

Representation | A number (magnitude) , direction using unit cap or arrow at the top and unit | A number (magnitude) and unit |

Symbol | Quantity Symbol in bold and an arrow sign above | Quantity symbol |

Direction | Yes | No |

Example | Velocity and Acceleration | Mass and Temperature |