# 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 â€“ vB

(Fig. 5). Similarly vBA = vB â€“ vA

Fig. 5
• If two bodies A and B are moving in straight line in opposite direction (Fig. 6), then

Fig. 6

vAB = vA + vB (towards B)

vBA = vB + vA (towards A)

vAB = â€“ 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 , i.e.,
• 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 â€“ vB and the relative velocity of B wrt A is given by vBA = vB â€“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 â€“ (â€“ vB) = vA + vB and the relative velocity of B wrt A is given by vBA = â€“ vB â€“ vA