Q1) Two cars A & B moving in same direction with vel. 30m/s & 20m/s respectively When car A is at a distance d behind B driver of A applies brakes producing uniform retardation of 2m/s². To avoid collision minimum distance d (b/w the cars) should be---

ans) here u_A=30m/s ,u_B=20m/s

         in a time tsec the body a retards with a acceleration =2m/s² n the final velocity b'coms zero 

         so applyin V =U +at for body A  

         v get  0=30+(-2).t

         then v get t=15sec

         so in t= 15 sec body A travels a distance

         d=Ut+1/2.at²= 30x15+1/2(-2)x(15)² =450- 225= 225 m

         whereas body B travels a distance S =U_Bxt = 20 x 15 =300 m

         so the minimum distance 'd'  required is 225m

         i think this might help u ........

relative velocty of A wrt B = 30-20 =10m/s

now the acc = -2 m/s^2 as the direction of both acc and rel velocity is diffrent

now to avoid collision they should just meet.........so......

0= 10^2 - 2*2*d

d= 100/4=25m