If you missed the first lecture. . .

1. If you missed the first lecture. . . • Find the course webpage:http://physwww.mcmaster.ca/~okon/1d03/1d03.html and read the course outline and the first lecture. • Log into Avenue to Learn (http://avenue.mcmaster.ca) and find Physics 1D03. There you can find out which lab/tutorial section you are in. • Get a copy of your lab/tutorial schedule from the course web page. Physics 1D03 - Lecture 2

2. Kinematics in One Dimension • Displacement, velocity, acceleration • Graphs • A special case: constant acceleration • Bodies in free fall Serway and Jewett Chapter 2 Physics 1D03 - Lecture 2

3. Kinematics : the description of motion • One dimension : motion along a straight line (e.g., the x-axis) Examples - sprinter running 100 meters in a straight line - ball falling straight down, and bouncing back up Physics 1D03 - Lecture 2

4. 1-D motion can be described by scalars (real numbers with units) as functions of time: Position x(t) (displacement from the origin) Velocity v(t) (rate of change of position) Acceleration a(t) (rate of change of velocity) • The sign (positive or negative) keeps track of direction (in 1-D). • Algebraic relations involving position, velocity, and acceleration come from calculus. • The same relations can be seen from graphs of position, velocity, and acceleration as functions of time. Physics 1D03 - Lecture 2

5. Displacement : x position x as a function of time t x2 x x1 t t1 t2 t Average velocity: (slope of the line) Physics 1D03 - Lecture 2

6. x Instantaneous velocity is the average over an ‘infinitesimal’ time interval : t t v is the slope of the tangent to the x vs. t graph. Physically, v is the rate of change of x, hence dx/dt. Physics 1D03 - Lecture 2

7. Acceleration is the rate of change of velocity: Physics 1D03 - Lecture 2

8. Graphs of x(t), v(t), a(t) Physics 1D03 - Lecture 2

9. Quiz A rubber ball is dropped and bounces twice from the floor before it is caught. (Take x to be upwards, and x=0 at the floor.) • At the highest point of the first bounce, vand a are: • a) both nonzero • b) one is zero, one is not zero • c) both zero • d) other (explain) Suggestion: Sketch graphs of x, v, a vs. time. Physics 1D03 - Lecture 2

10. Quiz • The particle’s average acceleration is positive • The particle’s average acceleration is negative • Not enough information to tell A particle (in one dimension) is initially moving. A few seconds later it has stopped (not moving). During that time interval: Physics 1D03 - Lecture 2

11. A Special Case: Constant Acceleration Use the definitions and derive Caution: These assume accelerationis constant. Exercise: eliminate t or a to show that These are sometimes convenient, but not necessary. They are valid only for constant acceleration. Physics 1D03 - Lecture 2

12. Example: Free Fall. (“Free fall” means the only force is gravity; the motion can be in any direction). • All objects in free fall move with constant downward acceleration, • This was demonstrated by Galileo around 1600 A.D. • “g” is called the “acceleration due to gravity” or the “gravitational field of the Earth”. Physics 1D03 - Lecture 2

13. The free-fall acceleration is the same for all objects; size and composition don’t matter. • But: • g varies slightly with location and height, about 0.03 m/s2 over the surface of the Earth, and up to a few kilometers above • if air resistance is significant, we don’t really have “free fall”. Physics 1D03 - Lecture 2

14. Quiz A block is dropped from rest. It takes a time t1 to fall the first third of the distance. How long does it take to fall the entire distance? • t1 • 3t1 • 9t1 • None of the above Physics 1D03 - Lecture 2

15. Quiz You throw a set of keys up to a window 4.00m above you. If the keys just make it to your friend on a balcony 1.0s later, what was their initial velocity ? • 40 m/s • 9.8 m/s • 4.5 m/s Physics 1D03 - Lecture 2