1. PHY 231 1 PHYSICS 231 Lecture 2: Motion in 1 dimension, part I Remco Zegers

2. PHY 231 2 Galileo (1564-1642) What mathematical forces govern accelerated motion? A wooden and stone sphere are dropped from the tower of pisa. Which one reaches the earth first? Answer: same time!

3. PHY 231 3 The inclined plane experiment Distance traveled goes with the square of time: x(t)~t 2 Time measured with water!

4. PHY 231 4 Displacement X=0 X=30X=45 t=0 t=1  X=30X=0 X=30X=45 t=0 t=1  X= - 30 Displacement is a vector and thus has direction (sign) Displacement is not equal to Distance

5. PHY 231 5 Average Velocity Average velocity= Displacement Time interval X=0 X=30X=45 t=0t=1t=2 t=0t=1 t=2 Which object has the largest average velocity over 2 s? Same!

6. PHY 231 6 Graphically x(m) t(s) The average velocity is the slope of the line connecting begin end end point in the x-t graph. Ignore what happens in between. = slope

7. PHY 231 7 Vectors and Scalars... X=0 X=30X=45 t=0 t=1  X= - 30 Average velocity:vector = - 30 = + 30 Average speed:scalar

8. PHY 231 8 Instantaneous Velocity “But officer, my average speed was only 25 miles per hour...” Sometimes we want to know the speed at one particular point in time.

9. PHY 231 9

10. 10 Instantaneous velocity x(m) t(s) What is the Velocity at t=2.0 s? Consider the average velocity for a very small time interval with t=2.0 s in the center!

11. PHY 231 11 Instantaneous velocity x(m) t(s) tt xx

12. PHY 231 12 Instantaneous velocity x(m) t(s) tt xx v=slope of the tangent to the x-t curve at t=2.0 s Think about the sign!

13. PHY 231 13 Question t x Which object had the largest average velocity? Which object had the largest instantaneous velocity? A B B B

14. PHY 231 14 Acceleration t x A change in slope in the x-t graph… t v …means a change in velocity: Acceleration

15. PHY 231 15 Acceleration Average acceleration Instantaneous acceleration:

16. PHY 231 16 Question t v t=0,v=20 t=1, v=5 What is the average acceleration between t=0 and t=1 A) 15 B) -15 C) 0 D) infinity

17. PHY 231 17 Constant positive velocity

18. PHY 231 18 Positive velocity and acceleration

19. PHY 231 19 Question Which v-t diagram matches which a-t diagram? GALILEO!