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Re: [Phys-l] Deltas in equations



For those for whom all this isn't obvious (limits of integration placed
after integral is performed.) delta t := t - t_o

V(t') = Int[a dt'')] = a* t' - a* t_o + v_o

X(t) = Int[ (a* t' - a* t_o + v_o) dt']

= (1/2)*(a*t^2 - a*(t_o)^2) - a*t_o*t + a*t_o*t_o + v_o* t - v_o*t_o +
x_o

= x_o + v_o*(delta-t) + (1/2)*a*[ t^2 + 2 t* t_o +(t_o)^2]

= x_ o + v_o(delta-t) + (1/2) * a * (delta-t)^2

Excuse the ascii

________________________
Joel Rauber
Department of Physics - SDSU

Joel.Rauber@sdstate.edu
605-688-4293



| -----Original Message-----
| From: phys-l-bounces@carnot.physics.buffalo.edu
| [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
| Of John Mallinckrodt
| Sent: Thursday, April 27, 2006 7:31 PM
| To: Forum for Physics Educators
| Subject: Re: [Phys-l] Deltas in equations
|
| On Apr 27, 2006, at 5:12 PM, Herbert Schulz wrote:
|
| > This, of course, is WRONG! If you do the integration you get
| >
| > x_f = x_i + v_i*(t_f - t_i) + (1/2)*a_x*(t_f^2 - t_i^2)
|
| Herb is right. This IS wrong. ;-)
|
| John "Slo" Mallinckrodt
|
| Professor of Physics, Cal Poly Pomona
| <http://www.csupomona.edu/~ajm>
|
| and
|
| Lead Guitarist, Out-Laws of Physics
| <http://www.csupomona.edu/~hsleff/OoPs.html>
|
|
|
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