A person is sitting on a moving train and is facing the engine. He tosses up a coin which falls behind him. The train is moving:
A) Forward and gaining speed
B) Forward and losing speed
C) Backward and losing speed
D) Backward and gaining speed

Hint: To solve this question we should under the concept of inertia and relative velocity. According to the concept of inertia, a body tries to maintain its state of motion or of rest unless an external force acts on it. The relative velocity of an object is its velocity with respect to another object or a frame of reference. We have to use the concept of relative velocity to find the velocity of the coin and conclude about the motion of the train.

Complete step by step answer:
Whenever we toss a coin, it has some initial velocity. The coin gets affected by the velocity of the train and hence its velocity can now be called relative velocity. The falling of a coin can be predicted on the basis of this relativity velocity.

If the train is accelerating, the coin in the air will land in a different place than the train is moving uniformly. That is, the velocity of the train increases in forwarding direction but the coin will fall behind the person because the distance travelled by train will be greater than that of the coin.

Also, when the train moves backwards, there is a decrease in the relative velocity of the coin and so when the person will toss the coin, the distance covered by the coin will be greater than that of the train. So here also the coin will fall behind the person.

So the coin will fall behind the man when the train is moving forward and gaining speed and when the train is moving backwards and losing speed.

Therefore Option (A) and (C) are correct.

Note: If the man is sitting in a train, moving with a uniform velocity and tosses a coin, the coin will fall at the same place. This happens because the initial velocity of the coin is the same as that of the train. so the relative velocity of the coin will be zero and hence both the train and the coin will travel the same distance at the same time.