Two cars approach each other; both cars are moving westward, one at 85 km/h, the other at 54 km/h. what is the magnitude of the velocity of the first car relative to (in the frame of reference of) the second car? answer in units of km/h.

Good afternoon.

In the reference of the second car, itself is stopped! It is the same thing as adding the opposite speed vector of this car to the rest of the world. See below:

Begginning:

    Car 1                  Car 2 
 → 85 km/h              → 54 km

Going to the referential of car 2, adding ← 54 km/h to both cars:

New Reference:

Car 1                                      Car 2
(→85 km/h) + (←54 km/h)       (→ 54 km/h) + (← 54 km/h)

Car 1                     Car 2
→ 31 km/h               0 km/h

So, relative to car 2, car 1 has a velocity of 31 km/h