Velocity & Displacement Notes October 2, 2018 Please write All eight questions Please write All eight questions Define “frames of reference” When is an object at rest? What is displacement? How is displacement different from distance? How is displacement calculated? How is velocity calculated? How are velocity and speed different? How are velocity and speed the same?

I. Motion The Universe is in constant motion. Every day, we see objects in motion – moving in different directions with different speeds. Motion is so common, it is sometimes difficult to analyze it in a “physics-sense.”

Motion, continued One-dimensional motion is the simplest form of motion. Example – a train on a straight track travels either forward or backward. We will study two-dimensional motion in a few weeks. Motion takes place over time and depends upon some frame of reference. The above mentioned train is at the first station, after a short time it will arrive at another station. However, the train is also on the Earth which is spinning on its axis, and the Earth is moving relative to the Sun, and the Sun (and the rest of the solar system) is moving through the Milky-Way galaxy, and the Milky-Way galaxy is moving relative…

Motion, continued When faced with a complex situation like motion, it will be easier to break it down into simpler parts. FRAME OF REFERENCE – a coordinate system for specifying the precise location of objects in space. In the case of the train, the stations along its route are convenient FRAMES of REFERENCE. If an object is at rest (not moving), its position does not change with respect to a frame of reference.

change in position = final position – initial position II. Displacement As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called the DISPLACEMENT of the object. Displacement is simply, a change in position. Displacement equation: Dx = xf – xi change in position = final position – initial position

Displacement, continued Displacement is NOT always equal to the distance traveled. Displacement is the change in position of the object, relative to its starting point. Distance is how far (total) the object has moved. Example #1: A space shuttle takes off from Florida and circles the Earth several times, finally landing in California. While the shuttle is in flight, a photographer flies from Florida to California to take pictures of the astronauts when they step off the shuttle. Who undergoes the greater displacement, the photographer or the astronauts? Who undergoes the greater distance, the photographer or the astronauts?

Displacement, continued Displacement can be positive: xf xi Dx = 30cm – 21cm = +9cm

Displacement, continued Displacement can be negative: xf xi Dx = 21cm – 30cm = -9cm

III. Velocity Speed and Velocity are NOT the same thing! Speed is how fast an object is moving. Velocity is how fast and in what direction an object is moving. Average velocity is displacement divided by the time interval. average velocity = change in position / change in time = displacement / time interval

Example #2: During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. Assuming that Andra ran in a straight line how far does Andra cover in 137 seconds? Given: v = 6.02 m/s Dt = 137 seconds Find: Dx Solution: Dx = vDt = (6.02 m/s)(137 s) = 824.74 meters, EAST

Velocity, continued Velocity is NOT the same as speed! Velocity has a magnitude and direction, this is called a vector. Speed has only a magnitude, this is called a scalar. Average Speed is equal to the distance traveled divided by the time of travel: Average Speed = distance / time.

Example #3 What is Jenni’s displacement? What is her distance?

Example #4 A book is moved once around the edge of a tabletop with dimensions 1.75 meters by 2.25 meters. If the book ends up at its initial position, what is its displacement? What is its distance? If it completes its motion in 23 seconds, what is its average velocity? What is its average speed? (you will have four answers!)

Example #4, answered Given: distance = 1.75m by 2.25 m time = 23 s Find: displacement, average velocity, & average speed Solution: Displacement = 0 meters Distance = 1.75m + 2.25m + 1.75m + 2.25m = 8 meters Average Velocity = 0 meters / 23 seconds = 0 m/s Average Speed = 8 meters / 23 seconds = 0.35 m/s