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Ben-CS
#16
Mar24-03, 12:33 PM
P: n/a
In the equation x = vt, v is a constant. Watch this:

Acceleration is constant:

(1.) a(t) = a_0

Integrating, we have velocity:

(2.) v(t) = a_0 * t + v_0

v_0 is the initial velocity. Integrating again, we have position:

(3.) s(t) = (a_0/2) * t^2 + v_0 * t + s_0

s_0 is the initial position. Note, if we let a_0 = 0, s_0 = 0, (3.) becomes this familiar expression:

(4.) s(t) = v_0 * t

This naturally implies that v(t) = v_0.


One needs to distinguish between constants, various types of functions, and dependent and independent variables.