1. Relative Motion

2. Frame of Reference (F.O.R.)
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.

3. Situation
Problem involving more than one object in motion
Example:

4. Solution
Use relative motion to reduce number of variables
Example:

5. Problem #1
Two cars are traveling down a highway in the same direction. Car A is traveling at speed v1 and currently a distance x behind Car B that is traveling at v2. Given that v1 > v2 express the time t it takes Car A to catch Car B in terms of v1, v2, and x. v1 A v2 B x

6. “Hard Solution” x1 = distance for Car A at time t
x2 = distance for Car B at time t
x1 = x2
x1 = v1t x2 = x + v2t
v1t = x + v2t
v1t - v2t = x
(v1-v2)t = x
Relative Speed

7. Problem #2
Two runners are sprinting to the finish line of a 200 m race. Runner #1 is traveling at 5 m/s and is accelerating at 0.7 m/s2. Runner #2 is traveling at 7 m/s and is accelerating at 0.2 m/s2. Runner #2 is currently 100 m from the finish line and Runner #1 is 110 m from the finish line. How many seconds after this point in time will Runner #1 catch Runner #2?

8. Use Quadratic Formula or Graphing
Solution
F.O.R. is Runner #2  vo=0, a1=0
Runner #1  vo= -2 m/s, a = 0.5 m/s2, xo= -10 m
When Runner #1 catches Runner #2 x=0
x = xo + vot + ½ at2
0 = (-2t) t2
Use Quadratic Formula or Graphing
Calculator to solve
t = -3.5 s and t = 11.5 s

9. Problem #3
Two boats are sailing toward a marina. Boat A is traveling at 8 m/s and is currently 50 m behind Boat B that is traveling at 6 m/s. How many seconds will it take Boat A to catch Boat B?
Same basic problem as #1