Question

Two trains of length $ 500 $ m and $ 1000 $ m moving in opposite direction with same speed crosses each other in $ 10 $ sec, find their speed:
(A) $ 75{\text{ m/s}} $
(B) $ 150{\text{ m/s}} $
(C) $ {\text{100 m/s}} $
(D) None of these

Answer 1

Hint: Here we will use the concepts of the velocity which is defined as the total distance travelled upon the time taken. First of all we will find the total distance travelled and will take the ratio of distance to time and then will simplify.

Complete step by step solution:
Let us assume that relative velocity be $ {v_1} + {v_2} = 2v $ (since we are given that both the trains move with the same speed)
Relative displacement can be given by the sum of the distances travelled by the two trains.
Relative displacement $ = 1000m + 500m = 1500m $
Now, using the formula for the velocity can be expressed as the distance travelled by the time taken.
Therefore, $ \text{Relative Velocity} = \dfrac{\text{Relative Displacement }}{\text{Time taken}}$
Place the values in the above expression –
 $ 2v = \dfrac{{1500}}{{10}} $
Simplify using the concept that the common multiples from the numerator and the denominator cancel each other.
 $ 2v = 150 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ v = \dfrac{{150}}{2} $
Common multiples from the numerator and the denominator cancels each other.
 $ v = 75m/s $
Therefore, the speed of each train is $ 75m/s $
Hence, from the given multiple choices, the option A is the correct answer.

Note :
Always remember that the term speed and velocity mean the same mathematically but in physics velocity is the vector quantity whereas the speed is the scalar quantity. Be good in multiples and simplification and always remember that the common factors from the numerator and the denominator cancels each other.