Uniform velocity and acceleration?

Question

a boy in moving train is facing the engine.He tosses a coin up which falls behind him.the train is moving forward with uniform velocity or uniform acceleration?

what woulld be the motion of ball if train had moved moved with other option?i mean if in the first case unform velocity is right what would be the motion of ball if train moves with uniform acceleration?

Answer 1

The right answer is uniform acceleration,

lets say tossed coin (or ball) takes time t to fall on floor.

the moment when it is tossed it has same velocity as train say u (in horizontal direction).

as soon as the coin (or ball) looses the direct or indirect contact with the train it moves in space on its own momentum, since no external force acting as far as its horizontal motion is concerned. thus horizontal distance travelled in time t is u*t

but train has acceleration a in horizontal direction and in direction same as its motion. thus distance travelled by train is u*t + 0.5*a*t2

thus numerical value of distance travelled bye train is always more than that travelled by tossed coin(or ball). (irrespective of time of fall which is governed by gravity)

and so the coin (or ball) falls behind boy.

if train had uniform velocity numerical value of distance travelled by train and that by tossed coin (or ball) be same (u*t) and boy would have caught the ball