Question

A car A is moving with a speed of 40 km/h. Another car B is moving with 60 km/h in the opposite direction to car A. What will be the relative speed of car B with respect to car A?
1. 40 km/h
2. 60 km/h
3. 100 km/h
4. 20 km/h

Answer 1

Correct Answer - Option 3 : 100 km/h

CONCEPT:

• Reference Frame: When we say an object has a certain velocity, then this velocity is with respect to some frame that is known as the reference frame.
• Generally, when we measure the velocity of an object, the reference frame is taken to be the ground or the earth.
  • For example, if you are inside a moving bus and the bus is moving at a speed of 50 km/hr, then your speed according to another passenger sitting on that bus is zero. According to him, you are not moving.
  • But if someone observes you from outside the bus, standing on the ground, according to him, you are moving with 50 km/hr as you are on the bus and the bus is moving with 50 km/hr.
• So, the motion observed by the observer depends on the location (reference frame) of the observer.

The  relative velocity of A with respect to B is given by

V_AB = V_A - V_B

where V_AB is the relative velocity of A with respect to B, V_A is the absolute velocity of A, V_B is the absolute velocity of B.

CALCULATION:

• Given that V_A = 40 m/s and V_B = - 60 m/s (-ve sign due to opposite direction)
• The relative speed of car B with respect to car A = V_BA

VBA = VB - VA

VBA = -60 - 40 = - 100 m/s

So the correct answer is option 3.