# Equations for relative velocity

by UglyNakedGuy
Tags: equations, relative, velocity
 P: 11 hello everyone, Can someone kindly show me the equation for relative velocity calculations? when i search for them via wikipedia, there is only one formula for collinear objects and they move to the same direction... so what if they move opposite to each? and what if their motions follow a curvature ... plz help :P
 Emeritus Sci Advisor P: 7,623 Try the sci.physics.faq http://math.ucr.edu/home/baez/physic.../velocity.html It's got a section on "non parallel velocities".
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,510 The equation you mention for "relative velocity" is: if object A is moving away from me at velocity u and object B is moving along the same line and in the same direction at speed v (both relative to me) then the speed of object A relative to B is given by $$\frac{u- v}{1+ \frac{uv}{c^2}}$$ If they are moving in opposite directions, replace "-v" with "+v". If they are not moving along the same line, draw a line between them and calculate their components of velocity parallel and perpendicular to that line. Apply the formula above to the parallel components only.
Mentor
P: 11,750
Equations for relative velocity

 Quote by HallsofIvy If they are moving in opposite directions, replace "-v" with "+v".
And replace "+v" with "-v". More concisely, reverse the sign of v everywhere in the equation.
P: 11
 Quote by HallsofIvy The equation you mention for "relative velocity" is: if object A is moving away from me at velocity u and object B is moving along the same line and in the same direction at speed v (both relative to me) then the speed of object A relative to B is given by $$\frac{u- v}{1+ \frac{uv}{c^2}}$$ If they are moving in opposite directions, replace "-v" with "+v". If they are not moving along the same line, draw a line between them and calculate their components of velocity parallel and perpendicular to that line. Apply the formula above to the parallel components only.

unfortunately, when I search on website, I was told the equation as:

$$\frac{u- v}{1- \frac{uv}{c^2}}$$

and it says if they go opposite directions, I need to replace the sign...if you think im paranoid :) , plz check here http://en.wikipedia.org/wiki/Relative_velocity

to be honestly, im not a guy with physics background, i just like it.... so this is confusing for me... could you plz help?

once again, thank you!

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