What is relative velocity?

Short Answer

Relative velocity is the velocity of one object as observed from another object that may also be in motion. It tells us how fast one object appears to move when viewed from another moving object. Relative velocity helps compare motions and understand how two objects move with respect to each other.

For example, if two cars move on a road, one car sees the other moving with a certain speed depending on their directions and speeds. If they move in the same direction, relative velocity decreases; if they move in opposite directions, relative velocity increases.

Detailed Explanation :

Relative Velocity

Relative velocity is an important concept in physics that helps explain how the motion of one object is viewed from another object that is also moving. In daily life, we often see objects moving differently depending on where we stand or how we move. Relative velocity helps us measure this difference by comparing the velocities of two objects.

In reality, there is no universal “rest” point for measuring motion. Every motion is measured relative to something. For example, passengers sitting inside a moving bus feel at rest relative to the bus, but a person standing on the road sees them moving. This idea forms the basis of relative velocity.

Meaning of Relative Velocity

Relative velocity is the velocity of one object with respect to another object. It shows how fast one object appears to be moving when viewed from another object.

If object A observes object B, the motion of B relative to A is called the relative velocity of B with respect to A. It depends on:

  • The speed of object A
  • The speed of object B
  • The direction of their motion

Since velocity is a vector (has magnitude and direction), relative velocity also depends on direction.

Mathematically, if two objects A and B have velocities VA and VB, then:

  • Relative velocity of B w.r.t A (VBA) = VB – VA
  • Relative velocity of A w.r.t B (VAB) = VA – VB

These two velocities are equal in magnitude but opposite in direction.

Understanding Relative Velocity Through Everyday Examples

Example 1: Two Cars Moving in the Same Direction

If Car A moves at 60 km/h and Car B moves ahead at 80 km/h, then the relative velocity of Car B w.r.t Car A is:

VBA = 80 – 60 = 20 km/h.

This means Car B appears to move only 20 km/h faster when viewed from Car A, even though its actual speed is 80 km/h.

Example 2: Two Cars Moving in Opposite Directions

If Car A moves at 40 km/h and Car B moves at 50 km/h in the opposite direction:

Relative velocity = 40 + 50 = 90 km/h.

Here, they appear to approach each other very quickly because they move in opposite directions.

Example 3: A Passenger in a Bus

A person sitting inside a bus feels like they are not moving relative to another passenger sitting nearby, but someone outside the bus sees them moving fast.
Inside bus → relative velocity = 0
Outside bus → actual velocity is observed

Example 4: A Boat Crossing a River

Boat velocity and water current velocity combine to give relative velocity. The boat appears to move differently for someone standing on the riverbank and for someone inside the boat.

Why Relative Velocity Is Important

Relative velocity is used in many real-life and scientific applications:

  1. Studying motion between vehicles
    Helps calculate when two vehicles will meet or how they appear to move relative to each other.
  2. Air navigation
    Pilots use relative velocity to adjust airplane direction while flying against wind currents.
  3. Ship and river motion
    Helps calculate how a boat moves in flowing water.
  4. Sports
    In games like cricket or football, relative motion helps understand how players and the ball move relative to each other.
  5. Physics problems
    Relative velocity is essential in solving problems involving multiple moving objects.

Characteristics of Relative Velocity

  1. Depends on frame of reference
    The motion observed depends on where the observer is standing or moving.
  2. Is a vector quantity
    It has both magnitude and direction.
  3. Can increase or decrease
    Depends on whether the objects move in the same or opposite directions.
  4. Can be zero
    If two objects move at the same speed in the same direction, their relative velocity becomes zero.
  5. Helps compare motion
    Makes understanding movement easier when more than one object is involved.

Relative Velocity in One Dimension

In straight-line motion, calculating relative velocity is simple:

  • Same direction → subtraction
  • Opposite direction → addition

This gives the relative rate at which the distance between two objects changes.

Relative Velocity in Two Dimensions

When objects move in different directions (not just forward or backward), relative velocity is calculated using vector addition. This is common in:

  • Aircraft motion with wind
  • Boats in rivers
  • Sports movements
  • Projectile problems

In such cases, relative velocity depends on angle and direction as well as speed.

Conclusion

Relative velocity is the velocity of one object as observed from another moving object. It helps us compare how two objects move with respect to each other. It changes depending on direction, speed, and the observer’s frame of reference. Understanding relative velocity is essential for solving motion problems, studying vehicles, and analysing real-life situations like flying airplanes or moving boats.