Relative Motion

Key Questions

If an object A moves with velocity vecv""_A and object B with vecv""_B, Then velocity of A with respect to B (As observed by observer B) is,

vecv""_(AB) = $\vec{v} {\text{_A - vecv}}_{B}$.

Explanation:

As an example, let us consider linear motion for simplicity and assume that our observations in one dimension holds for two and three dimensions. (By using vector notation, this happily turns out to be the case.)

Two cars A and B moving with velocities v""_A and v""_B.

Velocity of A as observed by a person sitting in car B is then naturally,

$v {\text{_(AB) = v""_A - v}}_{B}$

if v""_A is greater than v""_B.

The observer sees the car A going away (ahead) from it with speed v""_(AB).

If the opposite is the case, v""_(AB) is negative.

The car B goes ahead of A with the speed v""_(AB).

Extending what we observed here to three dimensions is trivial.
We just have to use vector notations for that. Other details remain unchanged.

• Relative motion is the velocity of one mass with respect to another, even though both may be moving with respect to an observer.

An easy way to think about this is if you are standing next to a highway and two cars go past, one at 50 MPH and the other at 52 MPH. Even though the motion of both cars is fast compared to you, the driver of each car looks at the other and sees that the relative motion of the two cars is only 2 MPH. Keeping relative speeds low on our highways is an important key to highway safety!