1. Kinematics in one-Dimension
Chapter 2
Kinematics in one-Dimension

2. Mechanics: study of the motion of objects, and the related concepts of force and energy.
Kinematics: how objects move
Dynamics: why objects move as they do
Particle & Translational motion

3. Reference frames Sun Moon Earth Moon Describing motion Reference frame
Orbit of Earth
Earth
Moon
Describing motion
Reference frame

4. Coordinate system
Specifying motion
Coordinate system
Rectangular coordinates
x-y-z coordinate axes x z o y
Position: (x, y, z)
1-Dimension → x axis

5. . . Position & displacement x o P Position of P → x
Motional equation：the t function of position
Displacement：the change in position
Distance traveled → s B A C

6. Average velocity
distance traveled
———————— time elapsed
Average speed =
displacement
—————— time elapsed
Average velocity =
Example1：average speed and average velocity in half period of circular motion (r, T).

7. Instantaneous velocity
Average velocity over an infinitesimally short time interval:
Velocity is the derivative of x with respect to t
Example2：A particle with a motional equation
x=t3–9t2 +15t+1 (SI),
a) When does the particle change its direction?
b) Displacement and distance traveled in 0~2s.

8. Acceleration
How fast the velocity is changing
The derivative of v with respect to t
or the second derivative of x with respect to t

9. Motion at constant acceleration
Moving in a straight line and the acceleration a is constant
e.g. free fall motion

10. More examples
Example3:
where A, ω, φ are constants, analyze the motion
Solution: It is a simple harmonic motion.

11. Example4: A particle passes the origin with v=1 at the initial time, and its acceleration is a=12t, what is the motional equation? (all quantities in SI units)
Solution:

12. Example5: A diver enters water with a vertical velocity v0, and his acceleration in water is a = -kv2, how does his velocity change in the water?
Solution:
Differential equation
Separation of variables