# plz answerthe headlight of a train of length 200m is switched on when it starts from rest with an acceleration of 0.5 m/s2After 20s its tail-light is switched on. An observer in a frame moving with a constant velocity parallel to the railway track observes that the two events occur at the same place. the velocity of this frame isA) 5 m/s in a direction opposite to the train's motionB) 10 m/s in a  direction opposite to the train's motionC) 5 m/s in the same direction of the train's motionD) 10 m/s in the same direction of trains motion

105 Points
13 years ago

Dear pratik,

The correct answer is 5 m/s in the opposite direction. (A)

Solution,

after 20s the the distance covered by the train is

s = 1/2( a t^2)

s = 1/2 *1/2 *20*20

s = 100 m

the velocity of the train after 20s is

v= u2 +2as                            (u = 0 , since starting from rest )

v2 = 2*0.5*100

v =10 m/s

so after 20 secs the head light of train covers 100 m distance and then the back light is switched on,in order to see both the actions in same time the observer should cover the 300 m distance in 20 secs relative to train and in opposite direction.

V of observer with respect to train should be = 300/20 =  - 15 m/s  (- sign for opposite direction)

- 15 = Vframe - Vtrain

- 15 = Vframe - 10

Vframe = - 5 m/s

Hence The correct answer is 5 m/s in the opposite direction. (A)

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.