Question

Two parallel rail tracks run north-south. On one track train A moves north with a speed of 54 km/h and on the other track train B moves south with a speed of 90 km/h. The velocity of train A with respect to train B is:
A. 10m/s
B. 15m/s
C. 25m/s
D. 40m/s

Answer 1

Hint: We will acknowledge the values of the speed of the trains A and B given in the question and change their unit from km/h to m/s. Then we will find out the velocity of train A with respect to train B though the formula of relative velocity. Refer to the solution below.

Formula used: ${V_{ab}} = {V_a} - {V_b}$

Complete Step-by-Step solution:


The speed of train A as per given in the question is ${v_A} = 54km/h = 15m/s$
The speed of train B as per given in the question is ${v_B} = 90km/h = 25m/s$
Since train B is moving in the opposite direction, so-
${v_B} = - 25m/s$
Since we know that the formula for relative velocity is ${V_{ab}} = {V_a} - {V_b}$. Thus,
The relative velocity of the train A with respect to train B is-
$
   \Rightarrow {v_{AB}} = {v_A} - {v_B} \\
    \\
   \Rightarrow {v_{AB}} = 15 - \left( { - 25} \right) \\
    \\
   \Rightarrow {v_{AB}} = + 40m/s \\
$
Hence, the relative velocity of the train A with respect to train B is $40m/s$.
Thus, option D is the correct option.

Note: We witness times when one or more objects move in a non-stationary frame when opposed with another observer. For instance, a boat crosses a river that flows at some pace or an airplane that encounters wind during its flight. In all such instances we need to consider the effect that the medium causes on the object in order to describe the complete motion of the object. In doing so, we calculate the relative velocity of the object taking into account both the velocity of the particle and the velocity of the medium. The relative velocity in the rest frame of another object or observer A is the velocity of an object or observer B.