Physics 151 Week 3 Day 2 Topics Motion Diagrams & Motion Graphs Motion Definitions Velocity to position Adding and Subtracting Vectors Graphically

Where’s the train? A train is moving at a steady 30 m/s. At t = 0, the engine passes a signal light at x = 0. Without using any formulas, find the engine's position at t = 1s, 2s, and 3s. Express your reasoning in words. Slide 2-34

Where’s the train? A train is moving at a steady 30 m/s. At t = 0, the engine passes a signal light at x = 0. Without using any formulas, find the engine's position at t = 1s, 2s, and 3s. Express your reasoning in words. EQUATION FROM GRAPH EQUATION FROM AREA Slide 2-34

Checking Understanding 1 Two runners jog along a track. The positions are shown at 1 s time intervals. Which runner is moving faster? Answer: A Slide 1-21

Answer Two runners jog along a track. The positions are shown at 1 s time intervals. Which runner is moving faster? A Answer: A Slide 1-22

Representations of Motion Motion diagram (student walking to school) Table of data Graph Slide 2-9

A. B. C. D. Checking Understanding 2 Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Answer: C A. B. C. D. Slide 2-13

Answer Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Answer: C C. Slide 2-14

A. B. C. D. Checking Understanding 3 A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? Answer: C A. B. C. D. Slide 2-15

Answer A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? Answer: C C. Slide 2-16

Acceleration Acceleration is: The rate of change of velocity The slope of a velocity- versus-time graph Slide 2-20

Ball on Ramps (From an Exam) A ball is released from rest at the point shown on the incline and speeds up. It then rolls onto a level section of track at constant speed, and then rolls onto a second incline with the same slope as the first where it slows down. The diagram below shows the location of the ball at several instants in time. NOTE: THIS IS NOT A STROBE PHOTOGRAPH OR MOTION DIAGRAM. Describe the motion of the ball as it moves from left to right Determine the average velocity of the ball from t = 2.1 s to t = 3.6 s. Determine the average speed of the ball from t = 0.6 s to t = 5.1 s. Determine the average acceleration, ax, of the ball as it goes up the 2nd incline (from t = 3.6 s to t = 5.1 s). Answer: B

Question Velocity vectors point in the same direction as displacement vectors. in the opposite direction as displacement vectors. perpendicular to displacement vectors. in the same direction as acceleration vectors. Velocity is not represented by a vector. Answer: A Slide 1-8

Answer Velocity vectors point in the same direction as displacement vectors. Answer: A Slide 1-9

Vectors Slide 3-9

Adding Vectors Graphically Slide 1-33

Adding Displacement Vectors Slide 1-31

Example: Adding Displacement Vectors Jenny runs 1 mi to the northeast, then 1 mi south. Graphically find her net displacement. Slide 1-32

Find the following resultants graphically Adding Vectors Find the following resultants graphically Answer: B Slide 1-7

Vector Subtraction Slide 3-10

Acceleration Vectors Slide 3-11

Checking Understanding Which of the vectors below best represents the vector sum P + Q?   Answer: A Slide 3-13

Answer Which of the vectors below best represents the vector sum P + Q?   Answer: A Slide 3-14

Checking Understanding Which of the vectors below best represents the difference P – Q?   Answer: B Slide 3-15

Answer Which of the vectors below best represents the difference P – Q?   Answer: B Slide 3-16

Ball on Ramps (From an Exam) A ball is released from rest at the point shown on the incline and speeds up. It then rolls onto a level section of track at constant speed, and then rolls onto a second incline with the same slope as the first where it slows down. The diagram below shows the location of the ball at several instants in time. NOTE: THIS IS NOT A STROBE PHOTOGRAPH OR MOTION DIAGRAM. Draw a motion diagram for the following motion On the diagram above, use a delta v diagram to help draw an arrow indicating the direction of the acceleration of the ball at point A. Answer: B

Example: Velocity Vectors Jake throws a ball at a 60° angle, measured from the horizontal. The ball is caught by Jim. Draw a motion diagram of the ball with velocity vectors. Slide 1-35