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Relative Speed and Velocity (2)
Relative Speed  
The diagrams below show two cars moving along the same straight road.  
 
The stated speeds are measured relative to point O which is a fixed point on the ground.  
   
Where necessary, we will use the following notation: vA(O) means speed of body A relative to point O  
   
So, here we have vA(O) = 40ms-1 and vB(O) = 30ms-1  
   
Knowing these two figures, what is the speed of car A relative to car B?  
   
In one second, A moves 40m along the road but B only moves 30m.  
So, in one second, A moves further away from B in the positive sense.  
Obviously, if we imagine our self to be in car A, we will see car B moving further away in the negative sense.  
In other words:  
vA(B) = +10ms-1 and vB(A) = -10ms-1  
   
This simple example illustrates that, in general, to find the relative speed of two bodies, we subtract their speeds relative to a third body.  
vB(A) = vB(O) - vA(O) = 30 - 40 = -10ms-1  
and  
vA(B) = vA(O) - vB(O) = 40 - 30 = 10ms-1  
   
Now consider a slightly more dangerous situation:  
   
Again, the speeds stated are relative to O (in other words, measured in a frame of reference fixed relative to the earth).  
Suppose we want to know the speed of car A relative to car B.  
vA(B) = vA(O) - vB(O) = -50 - 80 = -130ms-1  
which means, of course, that vB(A) = +130ms-1  
   
By the way, in case this all seems pretty obvious and intuitive, be warned... when Einstein looked at this more closely, he found it to need significant modification when the relative speeds involved are very great (see the Relativity sections).  
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