Motion (in 1 –D)

1. Motion(in 1 –D) Physics Ch. 3 Position, Speed, and Velocity

2. MOTION • Motionis a change in the position of a body or system with respect to time. • Position is the location of a body or system at a given time. • Motion can be mapped by a coordinate system. • Coordinate Systems show the original location of the body (it’s initial or zero point) and the direction in which the body moves. North, Up, (+) West, Left, Backward,(-) East, Right, Forward,(+) South, Down, (-)

3. DISPLACEMENT vs. DISTANCE • Displacementis the change in position of an object. • It is a vector quantity, which means it has magnitude & direction. • Objects at rest have a displacement of zero. • Distance is the total length an object traveled. • It is a scalar quantity, which means it only has magnitude. (Magnitude refers to the amount) • Displacement is NOT the same as the distance traveled.

4. Example:A man traveled from point A to B to C to D. What is his distance? 4m + 2m + 4m + 2m = 12m What is his displacement? He is back in his original position. A to B is 4m east C to D is 4m west→ 0 m they cancel each other out! B to C is 2m south D to A is 2m north → 0m they cancel each other out!

5. Equation for Displacement • ∆d = df – di • d stands for position • f is for final position • i is for initial position • Draw a picture of the situation. • Set-up your problem using two-column format

6. Sample Problems • Example #1: • If the starting position of an object is 50 m west and the final position is 150 m east, what is the displacement? • Example #2: • If the starting position is 200 m north and the final position is 75 m south, what is the displacement?

7. VELOCITY • Velocity: the quantity that measures how fast something moves from one point to another -or- How fast you can move in a specific direction. • Average Velocity: the total displacement divided by the time interval during which displacement occurred. • Instantaneous Velocity: The speed and direction of an object at a particular instance in time.

8. Speed Vs. Velocity • Speed is a SCALAR quantity – it has only magnitude • Average speed is the distance traveled divided by the time interval. • Velocity is a VECTOR quantity – it has magnitude & direction. • Average Velocity is the displacement of an object divided by the time interval. SPEED VELOCITY

9. Equations SPEED VELOCITY

10. Problem Solving RULES: • Must draw a picture (motion diagram) that includes vector arrows representing speed/velocity and direction. • Two Column Format: • Left Side - Make a list of your given and unknowns, write the equation. • Right Side - input your numbers (with units) into the equation, show how to solve the problem, box in your final answer.

11. Velocity & Speed Practice • Joe and Sue take a 45 minute walk along a straight road to a store 3.0 km away. What is their average speed in m/s? • A bus traveled on Newburgh Road from a bus stop on 8 mile south to a stop at 5 mile in 15 minutes (lucky for the bus all of the lights were green!). What is the bus’s average velocity? • Smitty drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway.

12. MOTION Diagrams • A motion diagram (or map) represents the position, velocity, and acceleration of an object at various clock readings. • Arrows called vectors are used to indicate the direction and magnitude of the object in motion. V V V V V

13. Velocity & P-T Graphs • You can determine the velocity of an object by finding the slope of position vs. time. • Slope = change in vertical coordinates (y axis) change in horizontal coordinates (x axis) • Slope = 30 m – 10 m = 20 m = 10 m/s 3 s – 1 s 2 s

14. 3.2 Position time graph

15. 3.2 Interpret a position time graph • The position versus time graph shows a boat traveling through a long canal. • The boat has to stop at locks for changes in water level. • a) How many stops does the boat make? • b) What is the boat’s average speed for the whole trip? • c) What is the highest speed the boat reaches?

16. Constant Speed • On this graph, a constant speed is a straight horizontal line.

19. Application: Slow-motion Photography • A video camera does not photograph moving images. • It takes a sequence of still images called frames and changes them fast enough that your brain perceives a moving image. • You can use an ordinary video camera to analyze motion in laboratory experiments.

20. Stop action photography is cool. • http://www.youtube.com/watch?feature=player_detailpage&v=m2QY1h2nal8

21. Graphs -Position-time Straight line = constant speed. • Slope tells velocity. (v = ∆d/∆t) • Positive slope is positive velocity (going forwards) • Negative slope is negative velocity (going backwards) • Horizontal line = zero slope = stopped • Change in slope means change in speed.

22. Graphs -Velocity-time • Horizontal line = constant speed (velocity) • Curved line = change in velocity (not constant) • Straight line (not horizontal) = constant change in velocity • Slope tells change in velocity • Positive slope = constant acceleration (speeding up) • Negative slope = constant acceleration (slowing down) • Areaunder curve = distance travelled • (v x t = d) m/s x s = m (when horizontal); • ½ v x t =d (when sloped) • Instantaneous velocity is tangent to curve at any point. • Avg velocity is found between two points.