If you missed the first lecture. . .

1. If you missed the first lecture. . . • Find the course webpage:http://physwww.mcmaster.ca/~okon/1b03/1b03.html and read the course outline and the first lecture. • Log into WebCT and find Physics 1B03. Here you can find out which lab section you are in. Labs start this week. • read Chapters 1-2 of your book. Physics 1D03 - Lecture 2

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

3. Kinematics : the description of motion in terms of space and time – ignores the agents that cause the 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. Motion: the change of object position with time Position: measure of where an object is, relative to some pre- defined point Displacement: change in position Distance: the distance between two positions Often, positions are measured from the origin x=0 Physics 1D03 - Lecture 2

5. 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. • 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

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

7. 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

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

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

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

11. x t v t a t Graphs of x(t), v(t), a(t) Notice the kinks and discontinuities – they rarely happen in the real world… Physics 1D03 - Lecture 2

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

13. 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

14. A Special Case: Constant Acceleration Using the definitions we can derive Caution: These assume accelerationis constant. Exercise: eliminate t or a to show that These are sometimes convenient. They are valid only for constant acceleration. Physics 1D03 - Lecture 2

15. 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. • The constant “g” is called the “acceleration due to gravity”. Physics 1D03 - Lecture 2

16. 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

17. 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

18. Practice Problems: Knight Chapter 2: Problems 1, 3, 9, 11, 13, 17, 19, 21, 31, 47, 53. Physics 1D03 - Lecture 2