1. Kinematics: The Mathematics of Motion
Readings: Chapter 2

2. Motion along a straight line
Can be illustrated by position-versus-time graph:
1 s
2 s
3 s
4 s x
Continuous (smooth) curve
Origin
(x=0) x 10 cm 20 cm 40 cm 70 cm 1 2 3 4
t(s)

3. Position graph x 1 sec 2 sec 3 sec 4 sec
Velocity is the same – zero acceleration 1 2 3 4
t(s)
Straight line – uniform motion – the same velocity
Velocity is the slope

4. Position graph: uniform motionx
Motions in opposite directions
t(s)

5. Uniform motion: motion with constant velocityx t v t

6. Uniform motion: application
Example: x
Find and t

7. Position graph

8. realistic
non-realistic

9. Instantaneous velocity
Very small
Instantaneous velocity:
If dependence is given, then
- derivative
Example:
Instantaneous velocity - slope

10. Finding position from velocity

11. v t
The displacement is the area, displacement is positive v t
Displacement is negative

12. Example:
Find the net displacement C D A B
area

13. x A C
Velocity is the slope B t

14. Velocity is the slope
Acceleration is the slope

15. Motion with constant acceleration
Motion with constant velocity:
Motion with constant acceleration:

16. Motion with constant velocity or constant acceleration
Motion with constant acceleration:
Useful relation:
then

17. Motion with constant velocity or constant acceleration
Motion with constant acceleration:

18. Free fall motion - motion with constant acceleration

19. Free fall motion - motion with constant acceleration
At final point: