Announcements: Read preface of book (pp. xii to xxiii) for great hints on how to use the book to your best advantage!! Labs begin week of Sept. 3 (buy lab manual). Bring ThinkPads to first lab (and some subsequent labs)! Questions about WebAssign and class web page? My office hours: M, W, F 12:00 pm - 1:00 pm, Olin 302. Pay attention to demos (may pop up in exams). Keep homework work sheets, etc (to prepare for exams).

TUTOR & HOMEWORK SESSIONS This year’s tutors: Landon Bellavia, Peter Rice, Wilson Cauley All sessions will be in room Olin 107 Tutor sessions in semesters past were very successful and received high marks from students. All students are encouraged to take advantage of this opportunity. MondayTuesdayWednesdayThursdayFridaySaturdaySunday 4-6 pm Peter Rice 4-6 pm Landon Bellavia 4-6 pm Peter Rice 6-8 pm Landon Bellavia 6-8 pm Landon Bellavia 6-8 pm Wilson Cauley 6-8 pm Wilson Cauley 6-8 pm Landon Bellavia

Kinematics: motion in terms of space and time (position, x; velocity, v; acceleration, a). We’ll mainly deal with constant acceleration. Derivatives: In this chapter we will only look at motion in one dimension. Chapter 2: Motion in One Dimension Reading assignment: Chapter 3 (coming up). Homework (due Wednesday, Sept. 5): Problems:Q1, 1, 3, 7, 9, 12, 16, 23, 29, 32, 40, 43, 45 (Boxed problems are in student solution manual.) Remember: Homework 1 due Monday, Sept. 3.

Position, Displacement and distance traveled Don’t confuse displacement with the distance traveled. Example: What is the displacement and the total distance traveled of a baseball player hitting a homerun? Displacement of a particle: Its change in position: x f final position x i : initial position Displacement is a vector: It has both, magnitude and direction!! Total distance traveled is a scalar: It has just a magnitude Position: Location of particle with respect to some reference point.

Velocity and speed Average Velocity of a particle:  x: displacement of particle  t: total time during which displacement occurred. Velocity is a vector: It has both, magnitude and direction!! Speed is a scalar: It has just a magnitude Average speed of a particle:

The position of a car is measured every ten seconds relative to zero. A)30 m B)52 m C)38 m D)0 m E)- 37 m F)-53 m Find the displacement, average velocity and average speed between positions A and F. Blackboard example 2.1:

Instantaneous velocity and speed Instantaneous velocity is the derivative of x with respect to t, dx/dt! Velocity is the slope of a position-time graph! The (instantaneous) speed (scalar) is defined as the magnitude of its (instantaneous) velocity (vector)

Blackboard example 2.2 A particle moves along the x- axis. Its coordinate varies with time according to the expression (a) Determine the displacement of the particle in the time intervals t=0 to t=1s and t=1s to t=3s. (b) Calculate the average velocity during these two time interval. (c) Find the instantaneous velocity of the particle at t=2.5s. (d) What is the instantaneous velocity at 1s (graph).

Acceleration When the velocity of a particle (say a car) is changing, it is accelerating (can be positive or negative). The average acceleration of the particle is defined as the change in velocity  v x divided by the time interval  t during which that change occurred.

The instantaneous acceleration equals the derivative of the velocity with respect to time (slope of velocity vs. time graph). Because v x = dx/dt, the acceleration can also be written as: Units: m/sec 2

Worksheet: Find the appropriate acceleration graphs parabola

Conceptual black board example 2.3 Relationship between acceleration-time graph and velocity-time graph and displacement-time graph.

Notice that acceleration and velocity often point in different directions!!!

One-dimensional motion with constant acceleration *Velocity as function of time *Position as function of time Position as function of time and velocity Velocity as function of position Derivations: Book pp These four kinematic equations can be used to solve any problem involving one-dimensional motion at constant acceleration.

Black board example 2.4 The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration of – 5.60 m/s 2 for 4.2s, making skid marks 62.4 m long ending at the tree. With what speed does the car then strike the tree?

Freely falling objects In the absence of air resistance, all objects fall towards the earth with the same constant acceleration (a = -g = -9.8 m/s 2 ), due to gravity.

Black board example 2.5 A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. The building is 50 m high. Using t A = 0 as the time the stone leaves the throwers hand at position A, determine: (a)The time at which the stone reaches its maximum height. (b) The maximum height. (c) The time at which the stone returns to the position from which it was thrown. (d) The velocity of the stone at this instant (e)The velocity and and position of the stone at t = 5.00 s. (f)Plot y vs. t; v vs. t and a vs. t

Review: Position x, velocity v, acceleration a Acceleration is derivative of v and 2 nd derivative of x: a = dv/dt = d 2 x/dt 2, and v = dx/dt. Know x, v, a graphs. v is slope of x-graph, a is slope of v graph. Kinematic equations on page (constant acceleration). Know how to use! Free fall (constant acceleration)