Question

Two cars A and B approach each other at the same speed, then what will be the velocity of A if the velocity of B is $8\,m{{s}^{-1}}$?
A. $8\,m{{s}^{-1}}$
B. $16\,m{{s}^{-1}}$
C. $-8\,m{{s}^{-1}}$
D. Can’t be determined.

Answer 1

Hint: This is a very simple question that checks your basic knowledge skill. In order to solve this problem, you should know the concept of relative velocity. You know that velocity is a vector quantity which has magnitude and direction as well.

Complete step by step solution:
Here in this question, it is given that two cars A and B are approaching each other with same velocity. So, it is clear that the magnitude of velocity will be the same for both. But we know that velocity is a vector quantity which has both the direction and magnitude. It is given that two cars are approaching each other means the direction of both are opposite to each other. Therefore, the negative sign is given which means they are moving in opposite directions.

Therefore, the answer is option C.

Additional information: Relative velocity is defined as the velocity of an object with respect to another observer. Velocity is a relative quantity. That is, velocity has only meaning when we consider two or more objects. Mathematically, we can quote that relative velocity is the rate of change of relative position of one particle with respect to another. Or else we can say that relative velocity is the vector sum of velocities of the measurable objects.

Note: Velocity and relative velocity are both measures of an object's speed and direction of movement. A static observer measures velocity. On a still frame, a still observer must be placed. However, a still frame is only an idea. All our regular measurements are done on the earth. We know that the earth revolves around the sun. There is always a centripetal acceleration toward the centre of motion when in an orbit. This implies that the Earth is not an inertial frame. However, for most of the calculations, we use Earth as a still frame. However, what we actually measure is the object's relative velocity to the earth.