Position vs. Time Graph Scalar vs. Vector Quantities September 21, 2017 Position vs. Time Graph Scalar vs. Vector Quantities

Drill – Take out HW from last night Draw a position vs. time graph for each scenarios: Demetrius ran out of his front door, then slipped and fell. He got up and walked the rest of the way to school. Sean walked from home up the steep hill opposite his house. He stopped at the top to put his skates on, then skated quickly down the hill, back home again. Breyana ran rapidly down the hill that starts at her house. She then slowed down as she climbed up the other side.

Position vs. Time Graph Can a position vs. time graph be used for all motion??? Only straight-line motion Not side to side Not up and down Linear line = constant speed Curved line = acceleration

Vocabulary Scalar quantity = quantity that tells you only the magnitude Examples: weight, speed Vector quantity = quantity that tells you magnitude and direction. Represented by letter with an arrow over it to signify that the quantity has a direction. Examples: velocity, acceleration

Scalar vs. Vector Quantities Name 3 examples of vector quantities. Name 3 examples of scalar quantities. What do vector and scalar quantities have in common? How are they different?

Scalar vs. Vector Quantities Identify the following quantities as a vector or a scalar: 55 mph 15 meters south 2.0 L 19.6 N down What is the magnitude of each of the quantities in question 1?

Vocabulary Speed = scalar quantity describing how fast something is moving in meters/second (v = d/t) Distance = scalar quantity that describes how far an object moves in meters

Average Velocity Vector quantity describing the rate that the position of an object is changing Speed + direction Symbol: v Units: m/s Relationship: average velocity = displacement/time vavg = Dx/t

Displacement Vector quantity describing an object’s change in position Concerned with the starting point and ending point of an object, NOT the path taken. Symbol: Dx Units: meters Dx = x2-x1

For the following graph… Write a scenario to describe the motion in the graph Calculate the speed of each segment Find the total distance Find the displacement

Example 1 Before a Ravens game you walk 7 blocks east to get chips and salsa at the store, then walk 4 blocks west to your friend’s house where you are going to watch the game. How far did you walk? What was your total displacement?

Example 2 During a punt return, the receiver has to drop back from the 20-yard line to the 5-yard line to field the ball. His teammates make some excellent blocks as he returns the ball straight up the field to the 35-yard line before getting tackled. How far did the punt returner travel during the play? What was his displacement?

Example 3 If it takes a student 25 seconds to walk 75 meters east down the hallway. What is their average velocity? *** When an object does not change direction the magnitude of the displacement equals the distance and the magnitude of the average velocity equals the average speed ***

Position vs. Time Graph Displacement Velocity September 22, 2017 Position vs. Time Graph Displacement Velocity

Drill Fill in the blanks with the appropriate vocabulary term: 1. The study of motion is called __________________. 2. Quantities which have both a magnitude and a direction are called __________________. 3. ____________ is a scalar quantity that describes how far something has traveled. 4. _____________ is a vector quantity that describes the position of an object. 5. ______________ describes how fast an object is moving and in what direction. 6. ____________ describes how quickly an object’s velocity is changing.

Displacement Vector quantity Displacement = object’s change in position Concerned with the starting point and ending point of an object, NOT the path taken. Displacement = final position – starting position Dx = x2-x1

Displacement Steps to solving displacement problems: Determine the starting position Map out the motion to determine the final position Displacement = final position – starting position Include units + direction *** Displacement is shortest path ***

Displacement – Alternate Method Steps to solving displacement problems: Determine the starting position Add up each segment of motion Forward motion is positive Backward motion is negative Include units + direction *** Remember Displacement = change in position ***

Motion Diagram Worksheet

Example 1 Starting from the origin a rabbit hops 25 meters north in 32 seconds then hops 28 meters south in 28 seconds. What is the total distance traveled by the rabbit? What is the rabbit’s total displacement?

Example 2 Starting from the origin a rabbit hops 35 yards north in 22 seconds then hops 65 yards south in 38 seconds. What is the total distance traveled by the rabbit? What is the rabbit’s total displacement? 3. What is the rabbit’s average speed? 4. What is the rabbit’s average velocity?

Example 3 A runner is standing 3 meters west of the starting line. From this position, she runs 37 meters directly east. At this point she stops to tie her shoe and walks west until she reaches the starting line. Once at the starting line, she runs 100 meters east. Time = 2:40 minutes What is the total distance she travelled? What is her displacement? What is her velocity?

Example 4 Can an object have a numerical distance, but a displacement of zero? Write a scenario where this is the case.

Distance, Displacement, Velocity worksheet