One Dimensional Motion. Motion in x or y only

Transcription

1 One Dimensional Motion Motion in x or y only

2 Scalar vs. Vector Scalar Defined as quantity with magnitude (size) only Example: 3 m, 62 seconds, 4.2 miles EASY Math!!! Vector Defined as quantity with magnitude and direction Example: 3 m west, 62 seconds at 45º, 4.2 miles Math is more complicated because you have to account for the direction!! We use + and to indicate direction!!!

3 Examples: Label each as scalar or vector: 1. 6 m/s west ft kg sec m mi/h m at 30º

4 Distance vs. Displacement Distance (d) SI unit is meter (m) Other units are ft, mile, etc, but WE use metric only! Scalar quantity, so math is easy!!! Defined as how far Example: Jordan walks 5m west then 15 meters east. What is her total distance? Displacement (Δx, Δy) SI unit is meter (m) Vector quantity, so direction matters! Defined as straight-line distance from end to start Example: Jordan walks 5m west then 15 meters east. What is her total displacement?

5 Speed vs. Velocity Speed (s) Defined as how fast Calculated as distance time SI units are m/s Scalar quantity s = d t Velocity (v) Defined as how fast and in what direction Calculated as displacement time SI units are m/s Vector quantity v = x t

6 Example: 1. Splat the cat runs 21.2 m north, 16.5 m south, and 10.7 m north again. What is Splat s total distance? What is Splat s displacement? 2. A car notices mile marker 72 as it rolls east past it. The car drives 68 miles east before turning around and speeding 16 miles west. Calculate the car s Position Distance travelled Displacement

7 Average speed / velocity We don t average these the way you do other values! v avg = total displacement total time s avg = total distance total time Example: Allie drives 800 miles, from Texas to Florida. She drives 90 mph for the first 100 miles. She gets busted and slows to 20 mph for the remaining 700 miles. 1. How long did it take her to get to Florida?

8 TX to FL, continued. 2. Calculate the average speed: Whereas, if I just average the speeds, I get 55 mph! WAY faster than Allie was going!!

9 Acceleration Defined as rate of change in velocity a = v = v f v i t t SI units are m/s 2 Vector quantity has a direction velocity acceleration Motion + + Speeding up + - Slowing down - - Speeding up - + Slowing down

10 Examples: 1. Splat the cat is running at 1.2 m/s when he speeds up to 3.7 m/s in 25.0 seconds. What is Splat s acceleration? 2. Cassie sprints from rest to 6.5 m/s at a rate of 0.57 m/s 2. How long did it take Cassie to reach this speed?

11 Distance vs Displacement Graphs

12 Graph Example: 1. Find velocity for each segment. 2. Graph v vs. t for the motion. 3. Calculate the average velocity. 4. Graph the a vs. t for the motion. 5. What is the velocity and position at 5 seconds? 6. Describe how a person would walk this graph.

13 Speed/Velocity Graphs

14 Graph Example: 1. Describe the motion of the graph. 2. What is the velocity, acceleration at 6 seconds? 3. Graph a vs t for this motion. 4. What is the total distance for the graph? 5. What is the displacement for the graph? 6. Graph d vs. t for this motion.

15 Acceleration graphs

16 Example: 1. Describe the motion of the graph. 2. What is the velocity change from 0 to.5 seconds? 3. What is the acceleration at 1.3 s? 4. What final velocity at 1.5 seconds, if initial velocity was 0.

17 Constant Acceleration Constant means same Equation: Use when this isn t given: v f = v i + at x v f 2 = v i 2 + 2a x t x = v i t at2 v f x = 1 2 v i + v f t a

18 Example: 1. Splat begins from rest and accelerates to 8.7 m/s in 14.2 seconds. What displacement did he travel? What was his acceleration? 2. When trying to bite me, Lucy the rabbit can move from 0.42 m/s to 4.9 m/s at a rate of 2.0 m/s 2. What distance did the rabbit travel? How long did it take the evil creature?

19 Freefall All objects within earth s atmosphere fall at the same rate of acceleration: 9.8 m toward the surface s 2 Same equations apply, but now I know a!! Equation: v f = v i gt v 2 f = v 2 i 2g x x = v i t 1 2 gt2 x = 1 2 v i + v f t a Use when this isn t given: x t v f

20 Examples: 1. Lucy the rabbit falls from the top of a building. If it takes her 1.92 seconds to fall to her demise, how tall was the building? 1b. How fast does she hit the ground? 2. What if Lucy fell from a building on the moon, where gravitational acceleration is only 1.6 m/s 2? How long would it take her to hit the ground from the same building?