Question

A man sitting on a train in motion is facing the engine. He tosses a coin up, the coin falls behind him. This means the train is moving:
A. forward with uniform speed
B. backward with uniform speed
C. forward with acceleration
D. forward with deceleration

Answer 1

Hint: We know that a body is said to be moving with a uniform speed if it covers equal distances in equal interval of time, and if the position of an object changes uniformly with time and speed increases with time then we say that it has an acceleration. So, to solve the given question we will use the following concept to find the required answer.

Complete step-by-step answer:
According to the question, when the coin is tossed it falls behind the man sitting in the moving engine, which means that the train is a non-uniform body and when the train is moving a pseudo force is acting on it. If the train would have been a uniform body then there would have no force acting on the coin.

Now, let us assume that the train is moving forward with an acceleration. In the man’s frame, a pseudo force is acting on the coin in backward direction which takes the coin in the backward direction with respect to the man. Thus, by the time, the coin reaches the floor of the train, it falls behind the man. Therefore, it means that the train is moving forward with an acceleration.

So, the correct answer is “Option C”.

Note: Acceleration of a moving object is determined by identifying two states of the moving object. Which gives us the initial velocity and time, and the final velocity and time. Once we determine the two states, we can apply the formula. i.e. $a = \dfrac{{v - u}}{t}$