# Relative Motion in One Dimension

- If two bodies
*A*and*B*are moving in straight line and same direction with velocity*V*and_{A}*V*, then relative velocity of_{B}*A*with respect to*B*is*v*=_{AB}*v*â€“_{A}*v*_{B}_{(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***v*=_{AB}*v*+_{A}*v*(towards_{B}*B*)*v*=_{BA}*v*+_{B}*v*(towards_{A}*A*)*v*= â€“_{AB}*V*_{BA}_{Same concept is used for acceleration also.}

# Some Important Notes

- Two cars
*A*and*B*are moving in same direction with velocity*v*and_{A}*v*(_{B}*v*>_{A}*v*). When_{B}*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*v*â€“_{AB}= v_{A}*v*and the relative velocity of_{B }*B*wrt*A*is given by*v*â€“_{BA}= v_{B}*v*_{A} - 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*v*â€“ (â€“_{AB}= v_{A}*v*) =_{B}*v*+_{A}*v*and the relative velocity of_{B}*B*wrt*A*is given by*v*_{BA}*= â€“ v*â€“_{B}*v*_{A}