What is Kinematics?

Kinematics is the study of motion of objects.
👉 It answers:

1. How fast?
2. How far?
3. In which direction?

👉 It does NOT deal with the cause of motion (that is Dynamics → Forces)

Types of Motion

Basic Quantities

Distance:

• It is defined as the distance travelled per unit time.
• Distance (d)Path length covered Scalar quantity (only magnitude). Unit: metre (m).
• Always positive or zero.

Displacement:

• Shortest distance from initial to final position.
• Vector quantity (magnitude + direction).
• Unit: metre (m).
• Can be positive, negative, or zero.

Relation:

• Relation: The magnitude of the displacement may or may not equal to the path of the path length traversed by an object.
• |Displacement| ≤ |Distance| .

• Displacement = Final – Initial = 1 m West

Speed and Velocity

Speed:

• Speed is a measure of how quickly an object moves from one place to another. It is defined as the distance travelled per unit time.
• Formula: Speed = Distance / Time
• SI Unit: metre per second (m/s), Other common units: kilometre per hour (km/h), miles per hour (mph)
• Explanation:
  • If a car travels 100 kilometres in 2 hours, its speed is 100km/2 hr = 50 km/h.
• Speed is a scalar quantity, meaning it only has magnitude (how fast), not direction.
• Rate of change of distance.
• Scalar quantity.

Average Speed:

• Average Speed is the total distance travelled divided by the total time taken, regardless of any variations in speed during the journey.
• Formula:Average Speed=Total Distance Travelled/Total Time Taken
• SI Unit: metre per second (m/s). (also commonly expressed in kilometres per hour (km/h))
• Key Points:
• It does not depend on the direction — it is a scalar quantity.
• It considers the entire journey, not just a particular moment.
• If an object moves at different speeds during different time intervals, average speed gives one overall value.
• Example:
  • A car travels: 60 km in 2 hours, then 40 km in 1 hour.
    • Total Distance = 60 km + 40 km = 100 km
    • Total Time = 2 hours + 1 hour = 3 hours
    • Average Speed=100 km/3 hr≈33.33 km/h

Velocity:

• Velocity is the rate of change of displacement of an object with respect to time. It tells us how fast and in which direction an object is moving.
• Rate of change of displacement.
• It may be positive or negative.
• It is a Vector quantity.
• Formula:
  Velocity = Displacement / Time

Uniform Velocity:

• An object is said to have uniform velocity if it covers equal displacements in equal intervals of time, in a fixed direction.
• In other words, both speed and direction remain constant.
• Example:
  A car moving at 60 km/h towards the north without changing speed or direction.
• Formula: v = Displacement/Time
• Non-uniform Velocity:
• An object has non-uniform velocity if it covers unequal displacements in equal intervals of time, or if its direction keeps changing.
• This means speed, direction, or both change with time.
• Example:
  • A car moving through traffic, changing speeds.
  • A car turning around a curve (direction is changing).

Relative Velocity:

• Relative velocity is the velocity of one object as observed from another moving object.
• It tells you how fast one object appears to move with respect to another.
• Formula:
  If two objects are moving in the same straight line:
  • V_relative= v₁ – v₂
• If both move in same direction, subtract the velocities.
• If both move in opposite directions, add the velocities:
  • V_relative= v₁ + v₂
• Example:
  • You are on a train moving at 80 km/h. Another train is moving at 100 km/h in the same direction.
  • Relative velocity = 100 – 80 = 20 km/h.

Acceleration:

• Rate of change of velocity.
• It is a Vector quantity.
• Formula: a = (v – u) / t
• where,
  • u = initial velocity,
  • v = final velocity ,
  • t = time.

• If velocity increases → Positive acceleration.
• If velocity decreases → Negative acceleration (Retardation or Deceleration)

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Rohit Thapa

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