Two points A and B start simultaneously along the line joining them in the same direction with acceleration of 1m/s2 and 2m/s2 and speed 3m/s and 1m/s respectively. Initially A is 10m behind B. What is the minimum distance between them?

both particle move relative to each other but after some time velocity of both particle will become equal for a instant..

.after this instant they will never come closer to each other....

Uab =2m/s        ( relative velocity of A wrt B)

Aab=-1m/s^2     (relative accleration of A wrt B)

V= u+at

Vab =0     ( finally)

t=2sec

this is the time when separation between them is minimum.......

distance travelled by first particle during this time is S1=2*3 +2=8m

distance travelled by second particle during this time is S2=2*1+4=6m

total relative displacement is 10 + 6-8 =8m

therefore minimum distance bw them will be 8m

Approved