# Relative Velocity in one dimension

• Motion of one body with respect to another is called concept of Relativity.
• Velocity of a body a with respect to velocity of “B” is VAB = VA - VB
• Velocity of an object with respect to itself is always zero.
• Relative velocity of approach of bodies moving towards each other with same velocity (v) is = 2v
• Relative velocity of separation of bodies moving away from each other with same velocity (v) is = 0.
• Relative velocity of a motion man swimming downstream V = Vm + VR (Vm = velocity of man VR = vet of River)
• Relative velocity of motion of man swimming up stream V = Vm - VR
• Time taken for down stream = \tt \frac{width\ of\ river}{V_{m}+V_{R}}
• Time taken for up stream = \tt \frac{width\ of\ river}{V_{m}-V_{R}}
• Any three dimensional coordinate XYZ axes system fixed to an object or event called reference frame.

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1. When two objects are moving in the same direction, then vAB = vAvB

2. When two objects are moving in opposite direction, then vAB = vA + vB

3. When two objects are moving at an angle, then v_{AB}=\sqrt{v_A^2+v_B^2-2v_{A}v_{B}\cos\theta}
and \tt \tan\beta=\frac{v_{B}\sin\theta}{v_{A}-v_{B}\cos\theta}