Motion in one dimension (chapter two)

1. Motion in one dimension (chapter two) • Motion diagrams, position-time graphs, etc. • Average and instantaneous velocity • Acceleration • Particle under constant acceleration • Freefall

2. Motion diagrams • Motion diagram:

3. Position vs. time • x vs. t

4. Velocity vs. time

5. Position vs. time • Demo - ~constant velocity • Conceptests • http://webphysics.davidson.edu/physletprob/ch7_in_class/in_class7_1/mechanics7_1_1.html • http://webphysics.davidson.edu/physletprob/ch8_problems/ch8_1_kinematics/default.html

6. Average velocity • only depends on beginning and end points and time interval • vector (scalar in 1-d only) • total displacement = integral of v(t)dt • examples: • A person runs 1 km in 5 minutes, then walks another 2 km in 20 minutes. What is their average velocity over the entire 3 km? • Using the velocity vs. time graph shown earlier, find the average velocity and the total displacement

7. Instantaneous velocity • limit of average velocity as interval goes to zero • tangent to x(t) - derivative of x(t) vs. t • examples • A ball rolling down a slope has a position described by the equation • What is the equation describing the instantaneous velocity? • ConcepTests

8. Particle under constant velocity relation between initial and final displacement comes from the definition of average velocity average equals instantaneous

9. Acceleration • average • instantaneous

10. Particle moving under constant acceleration From definition of average acceleration: Displacement of particle = integral of velocity as a function of time 

11. Particle moving under constant acceleration Combining previous two equations (removing a) Or (removing t)

12. Particle moving under constant acceleration • Wide range of applications • Zero acceleration: • Free fall: • acceleration due to gravity = 9.80 m/s2 downward (be careful about sign) • If we define up to be the direction of the positive y axis, the equations of motion for a particle in free fall are: Note that the velocity can be positive or negative

13. Particle moving under constant acceleration • ConcepTests • Demo – cart • More physlets • http://webphysics.davidson.edu/physletprob/ch8_problems/ch8_1_kinematics/default.html • Examples

14. Example - braking distance (from Giancoli, 2-10) • Estimate minimum stopping distance for a car traveling at 60 mph • 1) Maximum (negative) acceleration? 5~8 m/s2 (dry road, good tires) • 2) Typcial human response time? 0.3 ~ 1.0 sec (sober) • part 1 – distance before brakes applied: • part 2 – distance until car stops:

15. Example – Air bags (Giancoli 2-11) • If, instead of braking, the car in the previous example hit a tree, estiamte how fast the air bags need to inflate to do any good. • estimate a stopping distance ~ 1.00m • initial velocity = 26.8 m/s • final velocity = 0.00 m/s • first solve for a: • then find t

16. Problem solving • Choice of coordinate system can simplify problem • Be consistent with signs (direction of chosen axis) • Often problems involve two or more objects with some common variable (time, final displacement, etc.)