If two cars are moving in opposite directions with the same speed v, their relative velocity can be calculated by considering their velocities as vectors.
Let's assume the velocity of the first car is v₁ and the velocity of the second car is v₂. Since they are moving in opposite directions, the magnitude of their velocities will be the same, i.e., |v₁| = |v₂| = v.
To find their relative velocity, we subtract the velocity vector of the second car from the velocity vector of the first car:
Relative velocity = v₁ - v₂
Since both cars have the same magnitude of velocity v but are moving in opposite directions, we can substitute their velocities into the equation:
Relative velocity = v - (-v) = v + v = 2v
Therefore, the relative velocity of the two cars moving in opposite directions with speed v is 2v.