A question on special relativity

[choon_min]

hi, everone I am new here, here is my 1st question, hope anyone can help me.

As the relative law, speed of any object can't exceed speed of light, c.
If got one car A move to right with speed 0.8c and another car B move to left 0.8c. (if assume car can move so fast la..)

So, if i am the driver of car A, for my frame of reference the car B speed relative to me is 1.6c, which is more than c, violate with theory of relativity, so any problem here?

 

[Doc Al]

So, if i am the driver of car A, for my frame of reference the car B speed relative to me is 1.6c, which is more than c, violate with theory of relativity, so any problem here?

That's only true if you use Galilean addition of velocities, which is only accurate for small speeds:

$$V_{a/c} = V_{a/b} + V_{b/c}$$

The correct way to add velocities is to use the relativistic addition of velocities, which is correct for all speeds:

$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

Thus the speed of car B with respect to you will be 0.975 c, not 1.6 c.

Note that for small speeds (small compared to light speed), the formula for relativistic addition of velocity is well approximated by the Galilean addition of velocity formula.