More 1-D motion

1. More 1-D motion

2. Look at the x vs. t graph below:1. Write a ¶ describing the motion.2. Make a graph of velocity vs. time.

4. Look at the v vs. t graph below:1. Write a ¶ describing the motion.2. Make a graph of x vs. t.

6. Or

10. Now how do you find the velocity?

11. Tangent Line • To find the instantaneous velocity you must make a line that is tangent to the curve at the time you are interested in. • Tangent Line • A line that just brushes the curve and is parallel to the curve at that one spot. • Use any two points on tangent line to find slope. • Normal • The opposite of tangent. Perpendicular

12. Tangent at 4 seconds

13. Tangent at 7

14. v vs t • We can now make a graph of v vs t for all our data points.

15. What is the velocity at 4 sec? What is the velocity at 8 sec? How far has the object traveled during 0-4 seconds? How far has the object traveled during 4-8 seconds?

16. Can we make a graph of the slope of this line and if so what does it tell us?

17. We know that the slope of position gives us: The rate of change in position. • We call that velocity! • How much the position changes in every one second. • The slope of velocity gives us: The rate of change in velocity. • How much the velocity changes in every one second. • We call that acceleration!

18. Definition of Acceleration • Position is meters • Velocity is meters per one second or m/s • Acceleration is m/s per one second or m/s/s but is usually written as m/s2