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. 

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

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.

;dx dv

v adt dt

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: if xxx xf final position

xi: 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:

t

xvx

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:

timetotal

distance total speed average

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

dt

dx

t

xv

tx

0

lim

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 -4

-2

0

2

4

6

8

10

0 0.5 1 1.5 2 2.5 3 3.5 4

dis

pla

cem

ent

(m)

time (s)

t

x

(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).

2)2()4(2ttx

s

m

s

m

Acceleration

When the velocity of a particle (say a car) is changing, it is accelerating (can be positive or negative).

if

xixfxx tt

vv

t

va

The average acceleration of the particle is defined as the change in velocity vx divided by the time interval t during which that change occurred.

dt

dv

t

va xx

tx

0

lim

The instantaneous acceleration equals

the derivative of the velocity with respect to time (slope of velocity vs. time graph).

Because vx = dx/dt, the acceleration

can also be written as:

2

2

dt

xd

dt

dx

dt

d

dt

dva xx

Units: m/sec2

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

tavv xxixf *Velocity as function of time

2

2

1tatvxx xxiif *Position as function of time

Position as function of time and velocity

)(222ifxxixf xxavv Velocity as function of position

tvvxx xfxiif )(2

1

Derivations: Book pp. 36-37 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/s2 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/s2), 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 tA = 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 2nd derivative of x: a = dv/dt = d2x/dt2, 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 36-38 (constant acceleration). Know how to use!

• Free fall (constant acceleration)