Question

A 120 m long train is moving towards the west at a speed of $10ms^{−1}$. A small bird flying towards the east at a speed of $5ms^{−1}$ crosses the train. What is time taken by the bird to cross the train?

Answer 1

Hint
There are two different velocities that are covered by the train bird’s velocity and its own velocity. A body is said to have uniform velocity if it covers equal distance in equal intervals of time in a particular direction, however, the time intervals may be small.

Complete step by step answer
Given that, length=120m
speed=10m/s
According to the question ,The relative velocity of train with respect to bird is =(10+5)m/s
=15m/s
Since they are opposite to each other then addition will occur. The train is moving towards west and the bird flying towards east
Hence, in a frame of Reference in which bird is at rest the train is moving with velocity = 5m/s
The train is 120m long hence time taken for time to pass (from where bird is) end to end is,
$\Rightarrow Speed = \dfrac{d}{t}$ [Here d = distance , t = time]
$\Rightarrow t = \dfrac{{120}}{{15}}$
∴ t = 8sec.

Additional Information
Velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. There is a major difference between velocity and speed like, Speed, being a scalar quantity, is the rate at which an object covers distance. The average speed is the distance (a scalar quantity) per time ratio. On the other hand, velocity is a vector quantity; it is direction-aware. Velocity is the rate at which the position changes.

Note
In this type of questions always find out the total distance cover by the object and use the distance by velocity. It helps to find the time taken by the object. We should assume that both the trains run into its uniform velocity. A body is said to have uniform velocity if it covers equal distance in equal intervals of time in a particular direction, however, the time intervals may be small.