please ans fast step by step Two cars A and B are travelling in the same direction - Science - Force and Laws of Motion

Question

please ans fast step by step T w o c a r s A a n d B a r e t r a v e l l i n g i n t h e s a m e d i r e c t i o n w i t h v e l o c i t i e s v 1 a n d v 2 ( v 1 > v 2 ) W h e n t h e c a r B i s a t a d i s tan c e d a h e a d o f t h e c a r A , t h e d r i v e r o f t h e c a r A a p p l i e d t h e b r a k e p r o d u c i n g a u n i f o r m r e t a r d a t i o n a T h e r e w i l l b e n o c o l l i s i o n w h e n ( a ) d < v 1 - v 2 2 2 a ( b ) d < v 1 2 - v 2 2 2 a ( c ) d > v 1 - v 2 2 2 a ( d ) d > v 1 2 - v 2 2 2 a

Vipra Mishra · Accepted Answer

Dear Student

For the car A,

Initial velocity = v 1
Retardation = a
Distance it has to travel to avoid collision is = d
For car B,
Velocity of travel = v 2
Now,
The relative velocity of A with respect to B is, u = v
1 – v 2
The relative velocity becomes zero for the trains to avoid
collision That is, final relative velocity is, v = 0 [at this
moment the cars have equal velocity]
Now, using, v 2 = u
2 – 2as [negative sign appears since a
is retardation]
=> 0 = (v 1 – v 2 )
2 – 2ad
=> d = (v 1 – v 2 ) 2
/(2d)

So to avoid collision d should be greater than d >(v
1 – v 2 ) 2 /(2d)

Option d is right

Regards