# What is the correct formula for relative velocity?

I have consulted byjus.com, HC Verma and Khan academy, all are saying different. byjus and HC Verma book is saying that formula for relative velocity is $$V_a +V_b$$ but in Khan academy they are telling the formula is $$V_a - V_b$$.

So can you tell in what is the correct answer.
Here $$V_a$$ is velocity of one body and $$V_b$$ is velocity of other body.

• Treat the velocity as vectors not as scalars so v(r) = v(1)- v(2) where v(_) denotes vector corresponding to the velocity. – Aditya Garg May 26 at 12:57
• It'll be better if you quote the exact statement from the sources you have mentioned – Eagle May 26 at 13:34

If the two objects have the same velocity, their relative velocity should be zero. Therefore, you can see the correct formula is $$v_a - v_b$$.

Definition of relative velocity= Velocity of one obj with respect to another. Meaning that how fast an object is going if that second object is at rest.(from ground observer point of view)

Gen formula = Vab = Va-Vb meaning velocity of obj a if obj b is at rest but be careful of the sign convention.For ex if obj a and b are going in opp direction Vab =Va+Vb(the ground observer would think that if object b is at rest object a is drifting apart from b at velocity Va+Vb)

The formula you need to remember is $$\vec v_{A|B}=\vec v_A-\vec v_B,$$ where $$\vec v_{A|B}$$ is the relative velocity of A with respect to B. So in 1-D motion, the sign is - if motion is along same direction(magnitudes are subtracted), and it changes to + if motion is opposite (magnitudes are added). The formula is true in general even for motion in plane. You need to do vector subtraction. Just forget all others, and don't get confused.

I cannot find byjus.com and H C Verma stating the the relative velocity is $$V_{\rm a} + V_{\rm b}$$ and perhaps that is not surprising because the you have failed to define the quantities in your question precisely enough.

The equation is actually $$V_{\rm ag} = V_{\rm ab} + V_{\rm bg}$$

where $$V_{\rm ag}$$ is the velocity of $$a$$ relative to the ground, $$V_{\rm ab}$$ is the velocity of $$a$$ relative to $$b$$ and $$V_{\rm bg}$$ is the velocity of $$ab$$ relative to the ground.

Then rearranged this gives $$V_{\rm ab} = V_{\rm ag} - V_{\rm bg}$$ the equation given by the Khan Academy.

As a help to remembering the equation $$V_{\rm ag} = V_{\rm a\color{red}b} + V_{\rm \color{red}bg}$$ note how the "inner" two subscripts (in $$\color{red}{\rm red}$$) on the right hand side of the equation are the same and the "outer" two subscripts on the right hand side are the same as the subscripts on the the left hand side.

• Nice color effect! I learned a new Mathjax trick today! – Bill N May 27 at 12:12