The driver of a train moving with a constant velocity v1 along a straing track sights another train at a distance d ahrad of him on the same track moving in a same direction with a constant speed V2. He at once applies a brakes and gives his train a constant retardation f. There will be a collosioc of yhe trains if......?
a) v1 > V2 amd (V1 -V2)2 /2f < d
b) V1<V2 and (V1+V2)2 /2f > d
c) V1 > V2 and ( V1-V2)2 /2f > d
d) V1>V2 and (V12 - V22)/2f > d
The driver of a train moving with a constant velocity v1 along a straing track sights another train at a distance d ahrad of him on the same track moving in a same direction with a constant speed V2. He at once applies a brakes and gives his train a constant retardation f. There will be a collosioc of yhe trains if......?
a) v1 > V2 amd (V1 -V2)2 /2f < d
b) V1<V2 and (V1+V2)2 /2f > d
c) V1 > V2 and ( V1-V2)2 /2f > d
d) V1>V2 and (V12 - V22)/2f > d
For the train A,
Initial velocity = v1
Retardation = f
Distance it has to travel to avoid collision is = d
For train B,
Velocity of travel = v2
Now,
The relative velocity of A with respect to B is, u = v1 – v2.
The relative velocity becomes zero for the trains to avoid collision.
That is, final relative velocity is, v = 0 [at this moment the trains have equal velocity]
Now, using, v2 = u2 – 2fs [negative sign appears since a is retardation]
=> 0 = (v1 – v2)2 – 2fd
=> d = (v1 – v2)2/(2f)
For the train A,
Initial velocity = v1
Retardation = f
Distance it has to travel to avoid collision is = d
For train B,
Velocity of travel = v2
Now,
The relative velocity of A with respect to B is, u = v1 – v2.
The relative velocity becomes zero for the trains to avoid collision.
That is, final relative velocity is, v = 0 [at this moment the trains have equal velocity]
Now, using, v2 = u2 – 2fs [negative sign appears since a is retardation]
=> 0 = (v1 – v2)2 – 2fd
=> d = (v1 – v2)2/(2f)
