Relative Velocity — Definition

Definition

Imagine you are sitting in a train that is moving forward. If you look out the window and see another train moving in the same direction, but slower than yours, it appears to be moving backward relative to your train.

If it's moving faster, it appears to be moving forward. This everyday observation is the essence of relative velocity. In simple terms, relative velocity is how fast one object appears to be moving when viewed from another moving object, or from an observer who is also in motion.

It's not about how fast an object is moving compared to the ground (which we often call 'absolute' or 'ground' velocity), but rather how its motion is perceived by a moving observer.

To understand this better, let's consider a few scenarios:

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Objects moving in the same direction: — If car A is moving at $60,\text{km/h}$ and car B is moving at $40,\text{km/h}$ in the same direction, an observer in car B would see car A moving forward at $20,\text{km/h}$ ($60 - 40$). Conversely, an observer in car A would see car B moving backward at $20,\text{km/h}$ ($40 - 60 = -20$). The negative sign indicates the opposite direction.

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Objects moving in opposite directions: — If car A is moving at $60,\text{km/h}$ to the east and car B is moving at $40,\text{km/h}$ to the west, they are approaching each other. From car A's perspective, car B is approaching at a speed of $100,\text{km/h}$ ($60 + 40$). This is because their relative speed is the sum of their individual speeds when moving towards each other.

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Objects moving at an angle: — This is where it gets a bit more complex and requires vector subtraction. Imagine a person walking on a moving bus. The person's velocity relative to the ground is the vector sum of their velocity relative to the bus and the bus's velocity relative to the ground. Similarly, if rain is falling vertically, but you are running, the rain appears to be falling at an angle towards you. The velocity of the rain relative to you is the vector difference between the rain's velocity and your velocity.

The key takeaway is that velocity is always relative to a chosen 'frame of reference'. When we talk about 'absolute' velocity, we usually mean velocity relative to the Earth (which we consider stationary for most practical purposes).

Relative velocity simply shifts this frame of reference from the Earth to another moving object. It's a crucial concept for solving problems involving multiple moving bodies, like a boat in a river, an airplane in wind, or even a person trying to walk in the rain without getting wet.