Class Notes, Fall 2001

Week of   Aug 22   Sep 5 Oct 1 Nov 5 Phy 205 page
  Aug 27 Sep 10 Oct 8 Nov 12
    Sep 17 Oct 15 Nov 19
    Sep 24 Oct 22  Nov 26
      Oct 29    Notes for Fall, 2000

Phy 205, Week 3

5 Sep Velocity again. Re-write the previous development in terms of functional notation, x(t). Emphasize that this notation can be a little confusing, as it meant "x of t" not "x times t".

( x2 - x1 ) / ( t2 - t1 )   OR   ( x( t + Δt ) - x( t ) ) / Δt

t2 - t1 = Δt. To find the velocity AT a point still requires that you take these average values and let the time interval approach zero.

For an example take a function x( t ) = A + Bt + Ct2. Then

x( t + Δt ) = A + B ( t + Δt ) + C ( t + Δt )2

Put this into the definition of average velocity and simplify. The result is

B + 2 C t + C ( Δt )2

As the time interval approaches zero, this approaches B + 2 C t.

The acceleration of a car is sometimes expressed in terms of the amount of time it takes to go from zero to 60 mi/hr. This becomes a quantitative measure by taking the quotient:

[ 60 mi/hr - 0 ] / 5 sec = 12 mi/(hr sec)

To see how this compares to other accelerations I did some unit conversion to put this into a more standard form.

7 Sep Go over a couple of homework problems in some detail.
Velocity and acceleration in still more detail. The only two basic equations in chapter 2 of Young and Freedman are the equations (2-3) and (2-5). These are the definitions of velocity (in one dimension) and acceleration (in one dimension).
vx =
lim
Δ t -> 0 
 x( t + Δ t ) - x( t )
Δ t
 = dx
dt

ax =
lim
Δ t -> 0 
 vx( t + Δ t ) - vx( t )
Δ t
 = dvx
dt
You should think of everything else in chapter 2 as an application or an example or as some other special case. What I've written here isn't exactly what was the text has it because I expanded on the notation and wrote it out in more detail.

As a matter of notation, I am using vx for the velocity along the x-axis even though Young simply uses "v." The reason that I'm using the more extended notation is that in chapter 3 that's the notation that Young will use anyway. Why change? I went over the conceptual questions of signs that occur in the velocity and acceleration equation in the special case of falling under gravity. The sign for ax wasn't all that obvious.

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