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Relative Motion in One Dimension

  • If two bodies A and B are moving in straight line and same direction with velocity VA and VB, then relative velocity of A with respect to B is vAB = vA  vB
     
    (Fig. 5). Similarly vBA = vB – vA
     
    26944.png
     
    Fig. 5
  • If two bodies A and B are moving in straight line in opposite direction (Fig. 6), then
     
    26962.png
     
    Fig. 6
     
    vAB = vA + vB (towards B)
     
    vBA = vB + vA (towards A)
     
    vAB = – VBA
     
    Same concept is used for acceleration also.

Some Important Notes

  • Two cars A and B are moving in same direction with velocity vA and vB (vA >vB). When A is behind B at a distance d, driver in car A applies brake which causes retardation a in car A, then minimum value of d to avoid collision is 30033.png, i.e., 30027.png
  • A particle is dropped and another particle is thrown downward with initial velocity u, then
    • Relative acceleration is always zero.
    • Relative velocity is always u.
    • Time at which their separation is x is x/u.
  • If both the objects A and B move along parallel lines in the same direction, then the relative velocity of A wrt B is given by vAB = vA – vB and the relative velocity of B wrt A is given by vBA = vB –vA
  • If both the objects A and B move along parallel lines in the opposite direction, then the relative velocity of A wrt B is given by vAB = vA – (– vB) = vA + vB and the relative velocity of B wrt A is given by vBA = – vB – vA




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