2. Uniform Motion t (s) x (cm) v (cm/s) 0.0 1.0 5.0 5 2.0 10.0 3.0 15.0
0.0
1.0
5.0 5
2.0
10.0
3.0
15.0
4.0
20.0
25.0
6.0
30.0
7.0
35.0
8.0
40.0

3. Non-uniform motion t = 1 s t = 3 s t = 0 t = 2 s t = 9 s t = 4 s

4. What is the velocity at t = 5.5 s?
All we know from the given data is the average velocity between t = 5.0 and t = 6.0 s.
Measure the object’s position at a smaller time interval, like t = 5.4 s and t = 5.6 s.
Better yet, use t = 5.49 s and t = 5.51 s.
The velocity at the instant t = 5.5 s is approximately equal to the average velocity during a small time interval from t = 5.49 s to t = 5.51 s. But the best we can do with the given data is guess.
Chapter 2
Motion in 1-D
PHY211
Dr. Aaron Titus

5. Instantaneous Velocity
The velocity at an instant of time is called instantaneous velocity.
It is approximately equal to the average velocity measured during a very small time interval.

6. Position vs. time graph t (s) x (cm) 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0

7. Position vs. time graph t (s) x (cm) 0.0 1.0 0.5 2.0 2.2 3.0 5.0 4.0
0.0
1.0
0.5
2.0
2.2
3.0
5.0
4.0
8.8
13.8
6.0
19.9
7.0
27.2
8.0
35.4
9.0 45

8. Position vs. time graph
-Slope of a tangent line on an x vs. t graph is instantaneous velocity.
-Sign of slope (pos or neg) is direction of motion.
-How slope changes tells you whether it is speeding up or slowing down.

9. Example
Describe the motion of the object whose x vs. t graph is shown below.

10. Example
Describe the motion of the object whose x vs. t graph is shown below.

11. Velocity vs. time graph t (s) x (cm) v (cm/s) 0.0 1.0 0.5 2.0 2.2 1.8
0.0
1.0
0.5
2.0
2.2
1.8
3.0
5.0
2.8
4.0
8.8
3.8
13.8
6.0
19.9
6.1
7.0
27.2
7.3
8.0
35.4
8.2
9.0 45
9.6

12. Velocity vs. time graph t (s) x (cm) v (cm/s) 0.0 1.0 0.5 2.0 2.2 1.8
0.0
1.0
0.5
2.0
2.2
1.8
3.0
5.0
2.8
4.0
8.8
3.8
13.8
6.0
19.9
6.1
7.0
27.2
7.3
8.0
35.4
8.2
9.0 45
9.6

13. Velocity vs. time graph -Slope of v vs. t graph is acceleration.
-acceleration is the rate that the object speeds up or slows down.
-if slope is constant, then the motion is characterized by constant acceleration

14. Example
Describe the motion of the object whose v vs. t graph is shown below.

15. Example
Describe the motion of the object whose v vs. t graph is shown below.

16. Example
Describe the motion of the object whose v vs. t graph is shown below.

17. Observations
If the object’s velocity is positive and the object speeds up, its acceleration is:
positive
negative
zero

18. Observations
If the object’s velocity is positive and the object slows down, its acceleration is:
positive
negative
zero

19. Observations
If the object’s velocity is negative and the object slows down, its acceleration is:
positive
negative
zero

20. Observations
If the object’s velocity is positive and the object speeds up, its acceleration is:
positive
negative
zero

21. Position in meters
Poll
Car 1
t = 0
t = 1
t = 2
t =3
t =4
Car 2
t = 0
t = 1
t = 2
t =3
t =4
Car 3
t = 4
t = 3
t = 2
t = 1
t = 0
Car 4
t = 4
t = 3
t = 2
t = 1
t = 0
1. The positions of the cars above are shown at 1 s intervals from t = 0 s to t = 4 s. Which of these cars have negative accelerations during this 4 s time period?
A. Car 2 only B. Car 3 only C. Car 4 only
D. Cars 2 and E. Cars 2 and 4

22. Matching position and velocity graphs
Note what is being plotted in a given graph.
Describe the motion in words or with a diagram.
Sketch (or match) the graph that matches the motion diagram or verbal description of the motion.

23. The graph at left shows a moving object’s velocity v vs clock reading t. One of the graphs below shows the object’s position x plotted vs t over the same time interval. Which one is it? v t x A x B x C t t t D E x x t t