Login processing...

Trial ends in Request Full Access Tell Your Colleague About Jove

4.11: Relative Velocity in Two Dimensions

JoVE Core

A subscription to JoVE is required to view this content. Sign in or start your free trial.

Relative Velocity in Two Dimensions

4.11: Relative Velocity in Two Dimensions

Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is Image01, the position of P as measured in S′ is Image02, and the position of P as measured in S is Image03, which can be evaluated by utilizing vector addition as 


Also, the relative velocities are the time derivatives of the position vectors. Therefore,


The velocity of a particle relative to S is equal to its velocity relative to S′ plus the velocity of S′ relative to S. This can be extended to any number of reference frames.

For particle P with velocities Image04, Image05 and Image06 in frames A, B, and C, the relation can be stated as


Also, the relationship between the accelerations observed in two reference frames can be obtained by differentiating the velocity equation


This text is adapted from Openstax, University Physics Volume 1, Section 4.5: Relative Motion in One and Two Dimensions.


Relative Velocity Reference Frame Motion In Two Dimensions Particle Position Vector Addition Time Derivative Velocity Equation Acceleration Equation Openstax University Physics

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Waiting X
Simple Hit Counter