Relative Velocity

When objects move in a non-stationary frame about another observer, we encounter circumstances. A boat, for example, travels down a river at a given speed, or an aeroplane travels through the air while facing the wind. In all of these circumstances, the effect of the medium on the item must be considered to characterise the object’s overall motion. While doing so, we calculate the object’s relative velocity, considering both the particle’s and the medium’s velocity. In this article, we’ll learn how to determine relative velocity.

Relative velocity

We already know that speed is a function of time. The rate at which an object moves in conjunction with its direction is speed. When we talk about the velocity of one thing, however, we’re talking about the concept of relative velocity. What is relative velocity, exactly? The velocity of object A concerning another object B is called relative velocity.

The apparent velocity of object A relative to another object B is the apparent velocity of object A to an observer travelling with B.

Have you ever been on a train stopped at a station and noticed another train moving forward? Even though you were standing still, did you feel like you were travelling backwards?

The moving train (B) appears to be travelling at a velocity v, away from you, seated on the stationary train (A), or to a person on the platform. The platform appears to be disconnected from the halted train at the platform from a passenger’s perspective on the moving train travelling in opposing directions at the same speed or with the opposite velocity. We’re measuring velocity relative to an observer in all of these circumstances.

Comparing the relative velocities of objects moving in the same direction

The velocity of an object P is vP and the velocity of another object Q is vQ. The relative velocity of these objects in  moving in the same direction can now be calculated using the following equation: vPQ = vP – vQ 

The relative velocity of objects moving in the opposite direction

The velocity of an object P is vP and the velocity of another object Q is vQ. The relative velocity of these objects while  moving in the opposite  direction can now be calculated using the following equation: vPQ = vP + vQ

Dimension of Relative Velocity

Velocity has the same dimension as relative velocity and is given by the following: M⁰L¹T⁻¹

Examples of Relative Velocity

Here are two examples of relative velocity cases that can be expressed mathematically.

v2 < v1

 v2 > v1

Answer: When v1 > v2, the difference between the velocities will be negative, as will the difference x2 – x1 in the first example. After each time interval, the spacing between the two objects travelling about each other decreases by v1 – v2.

When v1 < v2, the difference between the velocities will be positive, as will the difference x2 – x1. After each time interval, the gap between the two objects travelling about each other increases by v1 – v2.

What Will Happen If Both Objects Travel at the Same Speed?

If both objects have the same velocity, then.

v12 = v2 − v1.

If v2 = v1, then x2 – x1 = 0, or x2 = x1, which means that these two objects will remain at the same relative distance apart, and so there will be parallel lines on the position-time graph.

Conclusion

The velocity of body A concerning body B, or vice versa, is referred to as relative velocity. The velocity of an object moving through a fluid, such as swimming or rowing, can also be calculated using relative velocity. When the wind speed and direction are known, relative velocity can also be determined concerning air. This can be used to measure the relative velocity of the javelin or shot put regarding the wind in outdoor sports like javelin throw or shot put.