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Two cars A and B are moving in the same direction with velocities $30$ m/s and $20$ m/s respectively. The relative velocity of A with respect to B is:
A$10$ m/s in the direction of motion of A
B$50$ m/s in the direction of motion of A
C$10$ m/s opposite to A's motion
DZero
Answer & Solution
Correct answer: A. $10$ m/s in the direction of motion of A
Relative velocity of A with respect to B: $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$.
With both cars moving the same way, magnitudes subtract: $|\vec{v}_{AB}| = 30 - 20 = 10$ m/s. The sign is positive in A's direction, so A appears to move forward at 10 m/s as seen from B's frame.
If the cars were moving toward each other (opposite directions), the formula becomes addition: $|\vec{v}_{AB}| = 30 + 20 = 50$ m/s (option B is the trap for that case).
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