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

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” +x (m) A car moves to the left as shown below. What is its displacement? t1t1 t2t2 Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

Here’s your sign… If position is +, what does it mean? If position is −, what does it mean? If displacement is +, what does it mean? If displacement is -, what does it mean? +x (m) 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. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus +x (m) A cat walks from x = +1 m to x = +4 m and then to x = −3 m. (1)What is the cat’s displacement? (2)What is the cat’s distance from where she started? (3)What distance does she travel?

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). 1.−6 m 2. 6 m 3.−8 m 4.8 m 5.−2 m

Poll Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus +y (m) 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? 1.13 m m 3.6 m 4.-6 m 5.1 m 6.None of the above

Poll Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus +y (m) 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? 1.13 m m 3.6 m 4.-6 m 5.1 m 6.None of the above

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. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus +x (m) If t 1 = 2.0 s and t 2 = 4.0 s, what is the average velocity of the car? t1t1 t2t2

Poll Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus A sprinter has a velocity of -10 m/s on the axis shown below. Which statement is definitely correct? 1.She is located on the left side of the origin. 2.She is located on the right side of the origin. 3.She is located on the right side of the origin and running left. 4.She is located on the left side of the origin and running left. 5.She is running to the left. 6.She is running to the right. +x (m)

Uniform Motion Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus t = 0 t = 1 s t = 2 s t = 3 s t = 4 st = 5 st = 6 s t = 7 s t = 8 s Constant Velocity

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? 1.40 m/s 2.20 m/s 3.10 m/s 4.5 m/s 5.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)? 1.40 yd line 2.30 yd line 3.10 yd line 4.zero (the goal line) 5.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? 1.  x direction 2.+x direction 3.It’s at rest.

Poll What is the velocity of the car? 1.30 m/s 2.  30 m/s 3.6 m/s 4.5 m/s 5.  5 m/s

Poll Which statement describes this x vs. t graph? 1.Dr. T drives at a constant velocity in the +x direction. 2.Dr. T drives at a constant velocity in the  x direction. 3.Dr. T is sitting in a parked car.

Uniform Motion (Problem Solving) Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus

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

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?

What is the velocity at t = 5.5 s? All we know from the given data is the average velocity between t = 5.0 and t = 6.0 s. Measure the object’s position at a smaller time interval, like t = 5.4 s and t = 5.6 s. Better yet, use t = 5.49 s and t = 5.51 s. The velocity at the instant t = 5.5 s is approximately equal to the average velocity during a small time interval from t = 5.49 s to t = 5.51 s. But the best we can do with the given data is guess. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus t = 0 t = 1 s t = 2 s t = 3 s t = 4 st = 5 s t = 6 s t = 7 s t = 8 s t = 9 s