Motion in One Dimension

1. Motion in One Dimension x t v t a Honors Physics Lecture Notes t

2. ConcepTest 2.3 Position and Speed 1) yes 2) no 3) it depends on the position If the position of a car is zero, does its speed have to be zero?

3. ConcepTest 2.3 Position and Speed 1) yes 2) no 3) it depends on the position If the position of a car is zero, does its speed have to be zero? No, the speed does not depend on position, it depends on the change of position. Since we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = –3 and be moving by the time it gets to x = 0.

4. Wednesday August 31th Introduction to 1-D Motion Distance versus Displacement

5. Average Speed • Average speed describes how fast a particle is moving. The equation is: • where: • = average speed • = distance • = elapsed time • The SI unit of speed is the (m/s). Average speed is always a positive number.

6. Average Velocity • Average velocity describes how fast the displacement is changing. The equation is: • where: • = average velocity • = displacement • = elapsed time • The SI unit of speed is the (m/s). Average velocity is + or – depending on direction.

7. x2 Dx x1 Dt t1 t2 AVERAGE VELOCITY The average velocity of a particle is defined as x Velocity is represented by the slope on a displacement-time graph t

8. Practice Problem: How long will it take the sound of a starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s.

9. Practice Problem: You drive in a straight line at 10 m/s for 1.0 km, then you drive in a straight line at 20 m/s for another 1.0 km. What is your average velocity?

10. Qualitative Demonstrations Demonstrate the motion of a particle that has an average speed and an average velocity that are both zero. Rock at Rest 2) Demonstrate the motion of a particle that has an average speed and an average velocity that are both nonzero. Rock Distance and Displacement are the same Demonstrate the motion of a particle that has an average speed that is nonzero and an average velocity that is zero. Rock moves in a Complete Circle 4) Demonstrate the motion of a particle that has an average speed that is zero and an average velocity that is nonzero. Does Not Happen

11. Quantitative Demonstration • You are a particle located at the origin. Demonstrate how you can move from x = 0 m to x = 5.0 m and back with an average speed of 0.5 m/s. • What is the particle’s average velocity for the above demonstration? 0.0 m/s, because displacement is 0.0 m.

12. Graphical Problem x t Demonstrate the motion of this particle. Rock at Rest

13. Graphical Problem x t Demonstrate the motion of this particle. Rock moving from rest with a positive constant velocity

14. Graphical Problem B x • A • t What physical feature of the graph gives the constant velocity from A to B? A Straight Line and slope

15. Graphical Problem: Determine the average velocity from the graph. X (m) 3.0 2.0 1.0 0.0 t (s) 2.0 4.0 6.0 -1.0 -2.0 -3.0

16. Graphical Review Problem x t Demonstrate the motion of these two particles. Blue Rock moving from rest at a higher constant velocity Red Rock moving from rest at a lower constant velocity

17. Graphical Problem x t Demonstrate the motion of these two particles. Blue Rock at rest, farthest from the origin (x = 0) Red Rock at rest, closest to the origin (x = 0)

18. Graphical Problem x t What kind of motion does this graph represent? Oscillatory motion, (almost) constantly changing velocity

19. Graphical Problem x A • 0.82m B • 0.22m t 0.75s 2.12s Can you determine the average velocity from the time at point A to the time at point B from this graph?

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