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

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

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

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

Position x(t) (displacement from the origin) 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

Average velocity : (slope of the secant line) 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

Instantaneous velocity is the average over an ‘infinitesimal’ time interval : x 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

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

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

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

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

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

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, v and 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

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

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

if air resistance is significant, we don’t really have “free fall”. 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

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

Practice Problems: Knight Chapter 2: Physics 1D03 - Lecture 2