Chapter 2, Problem 16STP

To determine

To Compare: The speed of one car relative to the other with speed of each car relative to the ground.

Explanation of Solution

Introduction:

Speed can be defined as the change in the position of the object with respect to time. Mathematically, given as:

  $v=\frac{s}{t}$

Here, $v$ is the speed

  $s$ is the distance travelled

  $t$ is the time taken.

According to the given statement, two cars approach each other. Hence, the relative motion always depends on the reference point between the two objects. In the given situation, consider two cars A and B. So, the speed of the car A relative to car B is $v_{AB}$ and the speed of car A with respect to the ground is $v_{AG}$ also the speed of car B relative to the ground is $v_{BG}$ .

Hence, the speed of car A relative to car B is given by:

  $\begin{array}{l}{v}_{AB}=v_{AG}-v_{BG}\\ v_{AB}=-\left(v_{BG}-v_{AG}\right)\\ v_{AB}=-v_{BA}\end{array}$

Conclusion:

Hence, the speed of the two cars relative to each other is compared with the speed of each car relative to the ground.