Motion in one dimension 2.1 Displacement and velocity

2-1 Objectives Describe motion in terms of displacement, time, and velocity. Calculate the displacement of an object traveling at a known velocity for a specific time interval. Construct and interpret graphs of position versus time.

Do Now - Notes Key terms and ideas notes Frame of reference Displacement distance Vector and Scalar Average velocity Velocity (instantaneous velocity) Velocity in a d. vs. t graph

Question How far do you travel to get to school in the morning? How do you compare this distance to the approximate straight-line distance between their home and school?

Distance vs. Displacement xi xf There could be many distances between xf and xi many be many, distance depends on the path. There is only one displacement between xf and xi. displacement refers to shortest distance between the xf and xi and direction from xi to xf Displacement = change in position = final position – initial position ∆x = xf - xi ∆ denotes change

Scalar vs. Vector SCALAR VECTOR A measured quantity that has NO DIRECTION Examples Distance, Time, Mass, Volume VECTOR A measured quantity that includes DIRECTION SIGN SHOWS DIRECTION Example Displacement

Example A man drives his car 3 miles north, then 4 miles east. Distance 7 mi 3 mi North Displacement 5 mi Somewhat Northeast What distance did he travel? What is his displacement from his point of origin?

Example Three men leave the same house on foot. The first man walks 30 feet north, then 40 feet west. The second man walks 90 feet south, then 88 feet north. The third man walks 10 feet east, then 50 feet west. Which man has traveled the greatest distance? Who is farthest from the house? Who is closest to the house? The second man The first man The second man

The frame of reference http://www.physics-chemistry-interactive-flash-animation.com/mechanics_forces_gravitation_energy_interactive/frame_of_reference_motion_child_ball_train.htm The choice of a reference point for the coordinate system is arbitrary, but once chose, the same point must be used throughout the problem. Text book, p41, figure 2-2, what would the displacement of the gecko be if the zero end of the meter stick had been lined up with the gecko’s first position?

Positive and negative displacement

How do you describe the speed of the car? The speed changes Average speed Instantaneous speed

Average Velocity vs. Average Speed change in DISPLACEMENT occurring over time Includes both MAGNITUDE and DIRECTION VECTOR The direction of the velocity vector is simply the same as the direction that an object is moving. AVERAGE SPEED change in DISTANCE occurring over time Includes ONLY MAGNITUDE SCALAR

Calculate Average Speed and Average Velocity The average speed during the course of a motion is often computed using the following formula: In contrast, the average velocity is often computed using this formula Does NOT include DIRECTION! The language of physics: ∆ means change

vavg = 3 mi / (8.3 min + 8.9 min + 9.2 min) Example Sally gets up one morning and decides to take a three mile walk. She completes the first mile in 8.3 minutes, the second mile in 8.9 minutes, and the third mile in 9.2 minutes. What is her average speed during her walk? vavg = d / t vavg = 3 mi / (8.3 min + 8.9 min + 9.2 min) vavg = 0.11 mi / min

Example Tom gets on his bike at 12:00 pm and begins riding west. At 12:30 pm he has ridden 8 miles. What was his average velocity during his ride? vavg = d / t vavg = 8 mi / 30 min vavg = 0.27 mi / min WEST

Example During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What displacement does Andre cover in 137 s? ∆x ∆t (∆t ) vavg = (∆t ) ∆x = vavg (∆t ) = (6.02 m/s)(137 s) = 825 m Answer: 825 m East

Class work Practice p. 44 #1-6

Interpret velocity in p-t graph What does this remind you of? SLOPE OF A GRAPH! What is happening in this graph? INCREASING SLOPE Moving with CONSTANT positive velocity Moving with INCREASING velocity Motionless Object CONSTANT POSITIVE SLOPE CONSTANT ZERO SLOPE

Graph interpretation of velocity Alert: Only use points on the line to calculate slope. Average velocity during 0-55 s Average velocity during 11-33 s

Distance vs. Time Graphs During what time interval was the object NOT MOVING? 2 – 3 seconds The interval on the graph where the distance remains constant!

Displacement vs. Time Graphs During what time interval(s) was the object to the left of the origin? During what time interval(s) was the object NOT MOVING? At what distance from the origin does the object stop? The object’s final position is at +1 meter (1 meter to the right of the origin) When the displacement is negative, the object has a position to the left of the origin 1 – 2 and 4 – 5 seconds Constant displacement means that the object doesn’t move

As the slope goes, so goes the velocity Slow, Positive, Constant Velocity Fast, Positive, Constant Velocity Fast, Negative, Constant Velocity Slow, Negative Constant Velocity

example Determine average velocity during 0-5 seconds The velocity is 5 m/s between 0-5 seconds The velocity is zero between 5-10 seconds

Displacement-time graph Distance-time graph Displacement-time graph NEVER decreases Read graph to find current total distance Subtract points to find distance traveled between them Average speed = slope or Δd/Δt curve = changing speed (acceleration or deceleration) increasing slope = increasing speed decreasing slope = decreasing speed Above x-axis = positive displacement from origin (east, right, up); Below x-axis = negative displacement from origin (west, left, down) Read graph to find current position. Difference between points = displacement traveled (change in position); Accumulate to get total distance velocity = slope or Δd/Δt positive slope = headed in positive direction from origin (east, right, up) negative slope = headed in negative direction from origin (west, left, down) curve = changing speed (acceleration or deceleration) increasing slope = increasing speed decreasing slope = decreasing speed

Distance vs. time graph

Displacement vs. time graph

Speed (Instantaneous Speed) and velocity (Instaneous Velocity) Speed, often means instantaneous speed - the speed at any given instant in time. It is often ref Velocity (Instantaneous velocity) - the speed at any given instant in time with direction at that instant The magnitude of Instantaneous velocity is always equal to the instantaneous speed The magnitude of average velocity can be less than the average speed.

Instantaneous velocity Text book p. 46 – figure 2-7 The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position versus time graph.

Average speed vs. instantaneous speed on p-t graph The slope of the secant line is between points A and B is the Average velocity between A & B B The slope of the tangent line is at point A is the instantaneous velocity at point A A

CLASS WORK Section Review Worksheet 2-1, “Displacement and Velocity.” Graph Skills