Unit 1 – One Dimensional Motion Part 1 – Describing Motion

1. Unit 1 – One Dimensional Motion Part 1 – Describing Motion

2. Kinematics The branch of mechanics that studies the motion of a body without caring about what caused the motion.

3. Some Physics Quantities Vector - quantity with both magnitude (size) & direction Scalar - quantity with magnitude only • Vectors: • Displacement • Velocity • Acceleration • Momentum • Force • Scalars: • Distance • Speed • Time • Mass • Energy

4. Mass vs. Weight • Mass • Scalar (no direction) • Measures the amount of matter in an object • Weight • Vector (points toward center of Earth) • Force of gravity on an object On the moon, your mass would be the same, but the magnitude of your weight would be less.

5. Quantity . . . Unit (symbol) Displacement & Distance . . . meter (m) Time . . . second (s) Velocity & Speed . . . (m/s) Acceleration . . . (m/s2) Mass . . . kilogram (kg) Momentum . . . (kg·m/s) Force . . .Newton (N) Energy . . . Joule (J) Units Units are not the same as quantities!

6. Kinematics – branch of physics; study of motion Position (x) – where you are located Distance (d) – how far you have traveled, regardless of direction Displacement (x) – where you are in relation to where you started Kinematics definitions

7. REPRESENTING MOTION Slide 1-3

8. Four Types of Motion We’ll Study

9. The Particle Model A simplifying model in which we treat the object as if all its mass were concentrated at a single point. This model helps us concentrate on the overall motion of the object.

10. Position and Time The position of an object is located along a coordinate system. At each time t, the object is at some particular position. We are free to choose the origin of time (i.e., when t = 0). Slide 1-17

11. Particle • Has position and mass. • Has NO size or volume. • Located at one point in space.

12. Position • Location of a particle in space. • One dimension (x) • Two dimensions (x,y) • Three dimensions (x,y,z)

13. 1-Dimensional Coordinates x = 1 m -1 0 1 2 3 X (m)

14. Distance • The total length of the path traveled by an object. • Does not depend upon direction. • “How far have you walked?”

15. xf = -1 m 1-Dimensional Coordinates Distance moved by particle is 2 meters. xi = 1 m -1 0 1 2 3 X (m)

16. Displacement • The change in position of an object. • Depends only on the initial and final positions, not on path. • Includes direction. • “How far are you from home?”

17. Displacement • Represented by x. • x = x2 - x1 where x2 = final position x1= initial position

18. xf = -1 m 1-Dimensional Coordinates Distance moved by particle is 2 meters. Displacement of particle is -2 meters. xi = 1 m -1 0 1 2 3 X (m)

19. Distance vs Displacement B 100 m displacement 50 m distance A

20. Checking Understanding • Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position? • –27 m • –50 m • 23 m • 73 m

21. Answer • Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position? • –27 m • –50 m • 23 m • 73 m

22. Checking Understanding Two runners jog along a track. The positions are shown at 1 s time intervals. Which runner is moving faster?

23. Answer Two runners jog along a track. The positions are shown at 1 s time intervals. Which runner is moving faster? A

24. Checking Understanding Two runners jog along a track. The times at each position are shown. Which runner is moving faster? They are both moving at the same speed.

25. Answer Two runners jog along a track. The times at each position are shown. Which runner is moving faster? They are both moving at the same speed.

26. Average Speed save = d t Where: save = rate (speed) d = distance t = elapsed time

27. Average Velocity vave = ∆x ∆t Where: vave = average velocity ∆x = displacement (x2-x1) ∆t = change in time(t2-t1)

28. Velocity vs Speed • Average speed is always positive. • Average velocity can be positive or negative depending direction. • Absolute value of velocity can be used for speed if the object is not changing direction.