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 velocityparallelto 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

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

v²  = 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 = V_{frame - Vtrain}

- 15 = Vframe - 10

Vframe = - 5 m/s

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

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