Question 1

What is the formula for the velocity of A relative to B?

Accepted Answer

The velocity of A relative to B is written v_A,B and is given by v_A,B = v_A − v_B. The velocities of A and B must be measured in the same frame of reference before applying the formula.

Question 2

Why does reversing one vehicle not necessarily reverse the relative-velocity vector?

Accepted Answer

Relative velocity is a vector difference of signed components, not a rule that always returns a difference of magnitudes. If the car is +20 m/s and the truck changes from +10 to −10 m/s, the result changes from +10 to +30 m/s; it does not simply flip to −10 m/s.

Question 3

What changes when you move to another frame of reference?

Accepted Answer

Another frame can assign a different velocity to the same vehicle because its coordinate system is moving. For these fixed-orientation translating inertial frames, the red-car-relative-to-truck vector remains +10 m/s in the +20 and +10 m/s example.

Question 4

Why is the truck stationary in the truck's frame?

Accepted Answer

The truck frame is translated with the truck, so the truck's origin remains fixed and its frame-relative velocity is exactly zero. In the +20 and +10 m/s case, the red car has velocity +10 m/s in that frame and appears to move forward.

Question 5

How is a relative-velocity triangle drawn?

Accepted Answer

Draw v_A and v_B with a common tail. The vector v_A,B = v_A − v_B runs from the head of v_B to the head of v_A. Equivalently, reverse v_B and complete the vector construction; for collinear motion, the parallelogram collapses into a straight line.

Relative Velocity: Who Sees Whom Moving?

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