A person was riding a bicycle on a straight road at 14 kilometers per hour. If another person was also riding a bicycle in the same direction at nine kilometers per hour, find the velocity of the second person with respect to the first.
Alright, in this example, we have two people, we’ll call them 𝑃 one and 𝑃 two, each riding a bicycle in the same direction along a straight road. Person one rides at 14 kilometers per hour and person two, at nine kilometers an hour. Our goal is to find the velocity of the second person with respect to the first. The idea, then, is that person one is our reference point. And from that reference, we want to know the velocity of person two. That is, we want to calculate what we can call 𝑣 sub 𝑃 two 𝑃 one. This is equal to the velocity of person two minus that of person one.
If we assume that velocities in the direction of 𝑃 one and 𝑃 two are positive, then that means, leaving off the units, that 𝑣 sub 𝑃 two minus 𝑣 sub 𝑃 one is nine minus 14. This equals negative five, which means that our final answer, which includes units, is negative five kilometers per hour.
Notice, by the way, that if instead of finding the velocity of the second person with respect to the first, we had switched it around and found the velocity of the first person with respect to the second, then we can represent that symbolically as 𝑣 sub 𝑃 one 𝑃 two, which would equal 14 minus nine. And we would get a result of the same magnitude but the opposite sign. We see then how important it is to get the order of the people right in this relative velocity calculation.