### Video Transcript

Two cars π΄ and π΅ are moving at 142 kilometers per hour and 19 kilometers per hour in opposite directions. Given that car π΄ is moving in a positive direction, determine its relative velocity with respect to π΅.

Okay, so here we have these two cars π΄ and π΅ moving in opposite directions, and weβre told the speeds of each of these cars. Speed, we can recall, is a scalar quantity. Itβs never negative, always zero or positive. Velocity, on the other hand, is a vector quantity. It can be negative. In this example, weβre told that the direction of positive motion matches the direction of car π΄. In terms of velocities then, we could say that the velocity of car π΄ is positive 142 kilometers per hour. And then since car π΅ moves in the opposite direction, it has a velocity of negative 19 kilometers per hour.

Our question asks us to solve for the relative velocity of car π΄ with respect to car π΅. We can represent this symbolically as π£ sub π΄π΅. When we compute the velocity of car π΄ relative to car π΅, we can imagine ourselves to be observers riding in car π΅. From that perspective, what, then, is the velocity of car π΄? Thatβs what the relative velocity of π΄ to π΅ is. To calculate this, weβll take the velocity of car π΅ and subtract it from that of car π΄.

And by the way, the order in which we do this subtraction is determined by the order of the subscripts in our symbol here. For example, if we wanted to calculate instead the relative velocity of car π΅ to car π΄, that would equal π£ sub π΅ minus π£ sub π΄. As our problem statement shows, though, itβs π£ sub π΄π΅, the relative velocity of car π΄ to car π΅, that we really want to know.

Leaving out the units at this step, π£ sub π΄ is positive 142 and π£ sub π΅ is negative 19. We get then 142 plus 19 or 161. And now we recall our units of kilometers per hour. Relative to an observer in car π΅ then, car π΄ is moving at 161 kilometers per hour.