1. Chapter 2.1 to 2.3 Kinematics in One Dimension
AP Physics C

2. Points vs. Function

3. Interpreting a Position Graph

4. Uniform Motion

5. The Math of Uniform Motion

6. Skating with Constant Velocity
(vx)A = DxA/DtA =“rise”/“run”
= (2.0 m)/(0.40 s) = 5.0 m/s
DxB = (0.0 m) - (1.0 m) = -1.0 m
(vx)B = DxB/DtB = (-1.0 m)/(0.50 s) = -2.0 m/s
Reality check:
(vx)A = 5.0 m/s » 10 mph
(vx)B = -2.0 m/s » -4 mph
Reasonable.

7. Motion Diagrams
Position
Velocity

8. Instantaneous Velocity
Position
A jet plane accelerates for takeoff

9. Using Motion Diagrams
Instantaneous velocity is the local slope of the curve.
Observation:
Any smooth curve becomes linear at a sufficiently high magnification.

10. Velocity from Graphical Position
ay>0
ay<0

11. Welcome to Calculus…
This is the Derivative!!!

12. Multiple Choice Question
Which of the green velocity vs. time graphs goes with this blue position vs. time graph?

13. Finding Position from Velocity
The figure shows the velocity of a drag racer. How far does the racer move during the first 3.0 s?
Solution:
The net distance traveled is the area under the velocity curve shown in blue. This is a triangle with sides 12 m/s and 3.0 s. The area of this triangle is: A = ½(12 m/s)(3 s) = 18 m.
Thus, the drag racer moves 18 m in the first 3 seconds.

14. Welcome to Calculus… This is the Integral!!!
Formal way to write this (don’t need to know this yet):
Conceptual way to think about this:

15. Finding the Turning Point
The figure shows the velocity of a particle that starts at xi= 30 m at time ti=0 s. 10
Draw a motion diagram for the particle.
Where is the particle’s turning point?
At what time does the particle reach the origin? 10 10 10 10
Solution:
The figure shows the motion.
The particle has zero velocity at t=2 s, which must be its turning point. Its position is x = x0 + 0∫2 v dt = 30 m + area of triangle from 0 to 2 s = 30 m + ½(10 m/s)(2 s) = 40 m.
To get to the origin, the particle must move -40 m from the turning point. This occurs at 6 s (see diagram).

16. Multiple Choice Question
Which of the blue position vs. time graphs goes with this green velocity vs. time graph? The particle’s position at ti = 0 s is xi = -10 m.