Motion is Relative Everything moves even though they may appear to be at rest

Frame of Reference Allows you to measure changes in position. A coordinate system for specifying the precise location of an object in space

Frame of Reference This diagram shows a change in position along the x-axis. What about the y-axis?How do I know?

Frame of Reference Positive and negative changes depend upon the frame of reference

Displacement Δx = x f - x i Change in position = final position – initial position

Displacement Does not always equal distance traveled

Displacement

A teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. Even though the teacher has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m). Yet when she is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m).

Displacement Example The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D. Determine the resulting displacement and the distance traveled by the skier.

Displacement Example Consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D. What is the coach's resulting displacement and distance of travel?

Scalar vs. Vector

Vectors Can be represented graphically

Scalar vs. Vector Example a. 5 m b. 30 m/sec, East c. 5 mi., North d. 20 degrees Celsius e. 256 bytes f Calories Determine whether the following are scalar or vector quantities. scalar vector scalar vector

Velocity Velocity is a vector

Velocity

Velocity Example Heather and Matthew walk eastward with a speed of 0.98 m/s. If it takes them 34 min to walk to the store, how far have they walked? Variables Equation Solve v = 0.98 m/s Δt = 34 min Δd = ?? v = ΔdΔd ΔtΔt =v Δt ΔdΔd Units don’t match! 34 min 1 min 60 s = 2040 s =(0.98 m/s)(2040 s) ΔdΔd = m = 2 km ΔdΔd

Instantaneous Velocity Velocity of an object at a specific point in its path

Acceleration Change in velocity over time constant velocity constant negative acceleration zero acceleration constant positive acceleration

Acceleration Acceleration is a vector!

Kinematics Δx = v i t + ½ at 2 v f 2 = v i 2 + 2aΔx Uniform Straight Line Acceleration v f = v i + at