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Relative Velocity

subtopicmedium~45 min study9 MCQ

Explains the concept of relative velocity in one dimension and its application.

Practice 9 questionsBack to syllabus~14 min

What is Relative Velocity?

The velocity of an object as observed from another moving object or frame of reference.

Key formula / rule: Relative Velocity (General)

Key points

  • Define relative velocity and explain its significance.
  • Apply the formula for relative velocity in one dimension.
  • Solve problems involving objects moving in the same or opposite directions.
  • Determine the time and position of meeting or crossing of two moving objects.

Common exam trap

Incorrectly applying the sign convention for velocities in 1D.

Definitions

Term

Relative Velocity

Meaning

The velocity of an object as observed from another moving object or frame of reference.

Term

Reference Frame

Meaning

A system of coordinates with respect to which the position and motion of an object are described.

Learning objectives

  • Define relative velocity and explain its significance.

  • Apply the formula for relative velocity in one dimension.

  • Solve problems involving objects moving in the same or opposite directions.

  • Determine the time and position of meeting or crossing of two moving objects.

  • Analyze motion from a non-inertial (but constant velocity) frame of reference.

Formulae

Name

Relative Velocity (General)

Note

Velocity of object A with respect to object B

Expression

vAB = vA - vB

Name

Relative Velocity (General)

Note

Velocity of object B with respect to object A

Expression

vBA = vB - vA

Name

Relative Position

Note

Relative position at time t

Expression

xAB(t) = xA(t) - xB(t)

Name

Relative Position (Constant Velocity)

Note

Relative position for constant velocities

Expression

xAB(t) = (xA(0) - xB(0)) + (vA - vB)t

Name

Relative Acceleration

Note

Relative acceleration of A with respect to B

Expression

aAB = aA - aB

Prerequisites

  • Basic understanding of displacement, velocity, and acceleration.

  • Vector addition and subtraction (especially in 1D with sign conventions).

  • Kinematic equations for uniformly accelerated motion.

  • Concept of a frame of reference.

Common mistakes

  • Incorrectly applying the sign convention for velocities in 1D.

  • Confusing vAB with vBA.

  • Forgetting that relative velocity is a vector subtraction, not always a simple scalar subtraction.

  • Not understanding the reference frame from which the velocity is being observed.

  • Assuming relative velocity is always less than individual velocities.

Keywords

  • Relative velocity

  • frame of reference

  • kinematics

  • one-dimension

  • speed

  • vector subtraction

  • meeting point

  • crossing time

Practice preview

  • A boat is moving downstream at 15 km/h. The river is flowing at 5 km/h. A bird flies upstream relative to the water at 10 km/h. What is the velocity of the bird relative to the ground?…

    hard

  • A police van is moving with a velocity of 10 m/s. A thief's car is moving with a velocity of 15 m/s in the same direction. The police van fires a bullet with a velocity of 100 m/s relative to the gun. What is the velocit…

    medium

  • Two trains, A and B, are moving on parallel tracks in the same direction with velocities 30 m/s and 20 m/s respectively. What is the relative velocity of train A with respect to train B?…

    easy

Practice 9 questions