One-dimensional motion Note that all definitions, terms, conclusions, and analysis applies to motion in a straight line, called one-dimensional motion. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Position In one dimension, the position of an object is its location on a number line (or axis). What is the position of this car? Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Displacement Displacement is the change in an object’s position. Δ means “change” “later” − “earlier” “final” − “initial” A car moves to the left as shown below. What is its displacement? t2 t1 +x (m) +1 +2 +3 +4 -4 -3 -2 -1 Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Here’s your sign… If position is +, what does it mean? If displacement is +, what does it mean? If displacement is -, what does it mean? +x (m) +1 +2 +3 +4 -4 -3 -2 -1 Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Distance Distance is the absolute value (magnitude) of the displacement. It tells you how far the object moved from its initial position. It does NOT tell you what direction it moved. If the object changes direction, then “distance traveled” is NOT the same as the absolute value of the displacement. A cat walks from x = +1 m to x = +4 m and then to x = −3 m. What is the cat’s displacement? What is the cat’s distance from where she started? What distance does she travel? +x (m) +1 +2 +3 +4 -4 -3 -2 -1 Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Poll A car moves from x = −8 m to x = −2 m. What is its displacement? Sketch a picture showing the object, its initial position, final position, and displacement (arrow). −6 m 6 m −8 m 8 m −2 m

Poll You toss a ball vertically into the air. It leaves your hand at y = -2 m, reaches its peak at y = 4 m, and is caught at y = -3 m. What is its displacement from the point where it left your hand to the point where you caught it? +y (m) -1 -2 -3 -4 +4 +3 +2 +1 13 m -13 m 6 m -6 m 1 m None of the above Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Poll You toss a ball vertically into the air. It leaves your hand at y = -2 m, reaches its peak at y = 4 m, and is caught at y = -3 m. What distance does the ball travel? +y (m) -1 -2 -3 -4 +4 +3 +2 +1 13 m -13 m 6 m -6 m 1 m None of the above Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Average Velocity An instant of time is measured by looking once at your watch. A time interval is measured by looking twice at your watch and calculating the time elapsed. If t1 = 2.0 s and t2 = 4.0 s, what is the average velocity of the car? t2 t1 +x (m) +1 +2 +3 +4 -4 -3 -2 -1 Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Poll A sprinter has a velocity of -10 m/s on the axis shown below. Which statement is definitely correct? +x (m) +1 +2 +3 +4 -4 -3 -2 -1 She is located on the left side of the origin. She is located on the right side of the origin. She is located on the right side of the origin and running left. She is located on the left side of the origin and running left. She is running to the left. She is running to the right. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Uniform Motion Constant Velocity t = 0 t = 1 s t = 2 s t = 3 s t = 4 s Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Graph x vs. t

Poll A sprinter’s position as a function of time is shown in the graph. What is the sprinter’s velocity? 40 m/s 20 m/s 10 m/s 5 m/s None of the above

Poll A football player’s position as a function of time is shown in the graph. If the goal line is defined to be x=0, what yard line was this football player at when the stopwatch was started (t=0)? 40 yd line 30 yd line 10 yd line zero (the goal line) None of the above

Poll A car moves according to the graph shown. If the +x direction is defined to be “to the right” (as has been our convention so far), in what direction is the car moving? x direction +x direction It’s at rest.

Poll What is the velocity of the car? 30 m/s 30 m/s 6 m/s 5 m/s

Poll Which statement describes this x vs. t graph? Dr. T drives at a constant velocity in the +x direction. Dr. T drives at a constant velocity in the x direction. Dr. T is sitting in a parked car.

Graph v vs. t t = 0 t = 1 s t = 2 s t = 3 s t = 4 s t = 5 s t = 6 s

The graph at left shows a moving object’s position x vs clock reading t. Which of the graphs below shows the object’s velocity v vs. t over the same time interval? x t A B C v v v t t t D E v v t t

The graph at left shows a moving object’s position x vs clock reading t. Which of the graphs below shows the object’s velocity v vs. t over the same time interval? x t A B C v v v t t t D E v v t t

Uniform Motion (Problem Solving) Identify the “main idea” of the problem if it is readily apparent. For example, “uniform motion.” Draw pictures, label objects, write knowns and unknowns. Use subscripts with variables. Write physics equations, definitions, and laws that might help solve the problem. Do the math. Check your work. Does the answer make sense?

Example An distance runner runs 400 m in a straight line in 60 s. Assuming she runs in the +x direction at a constant speed, what did the stopwatch read when she was 120 m from where she started?

Example In the 2008 Olympics, Michael Phelps swam the 100-m butterfly in 50.58 s. The second-place finisher was Milorad Cavic, 0.01s behind Michael Phelps. Assuming that they swim at the same constant velocity, how far ahead was Phelps when he touched the wall?

Example A corvette travels in the +x direction at 50 mi/h. A Volkswagon bug is initially 200 mi from the Corvette and travels in the x direction at a speed of 40 mi/h. At what position and at what time (clock reading) do they meet?