Final answer:
The relative speed of objects moving in opposite directions is the sum of their individual speeds because velocities are vectors that add like regular numbers in one-dimensional motion.
Step-by-step explanation:
The relative speed of objects moving in opposite directions is the sum of the individual speeds because velocity is a vector quantity, which means it has both magnitude and direction. When we deal with one-dimensional motion, the addition of velocities is straightforward: they add like regular numbers. If two objects are moving in opposite directions relative to a stationary observer, their speeds will add up. For example, if one car is moving at 40 km/h to the east and another car is moving at 60 km/h to the west, the relative speed of the cars with respect to each other would be 100 km/h.
Object velocities are added using vector addition rules, and when the vectors represent speeds in opposite directions, they are assigned opposite signs. Thus, for objects moving in opposite directions, we actually add the magnitudes of these velocities to find the relative speed.
It’s important to distinguish between speed, which is scalar, and velocity, which is a vector. The relative velocity is dependent on both magnitude and direction, which is why two objects moving towards each other effectively approach one another faster than if they were moving in the same direction.