Mathomatic version 14.2.1 (www.mathomatic.org)
Copyright (C) 1987-2008 George Gesslein II.
100 equation spaces available, 960K per equation space.
HTML color mode enabled.
1—> ; Suffixes: a=average, i=initial, t=terminal (final)
1—> ;
1—> ; M=mass
1—> ; A=acceleration
1—> ; f=force
1—> ; V=velocity
1—> ; P=position
1—> ; t=time
1—> ;
1—> ; Starting equations
1—> f = Ma A ; class force equation
#1: f = Ma·A
1—> Ma = (Mi + Mt) / 2 ; average mass
(Mi + Mt)
#2: Ma = —————————
2
2—> Va = (Vi + Vt) / 2 ; average velocity
(Vi + Vt)
#3: Va = —————————
2
3—> Vt = Vi + A t ; final velocity
#4: Vt = Vi + (A·t)
4—> Pt = Pi + Va t ; final position
#5: Pt = Pi + (Va·t)
5—> ;
5—> list all
#1: f = Ma*A
#2: Ma = (Mi + Mt)/2
#3: Va = (Vi + Vt)/2
#4: Vt = Vi + (A*t)
#5: Pt = Pi + (Va*t)
5—> 1 ; Integrate avg. mass to force equation.
#1: f = Ma·A
1—> eliminate Ma using 2
Solving equation #2 for (Ma) and substituting into the current equation...
(Mi + Mt)·A
#1: f = ———————————
2
1—> 4 ; Integrate force equaation to final velocity.
#4: Vt = Vi + (A·t)
4—> eliminate A using 1
Solving equation #1 for (A) and substituting into the current equation...
2·f·t
#4: Vt = Vi + —————————
(Mi + Mt)
4—> simplify
2·f·t
#4: Vt = Vi + —————————
(Mi + Mt)
4—> 5 ; Integrate avg. velocity to postion equation.
#5: Pt = Pi + (Va·t)
5—> eliminate Va using 3
Solving equation #3 for (Va) and substituting into the current equation...
(Vi + Vt)·t
#5: Pt = Pi + ———————————
2
5—> simplify
t·(Vi + Vt)
#5: Pt = Pi + ———————————
2
5—> ;
5—> ; ================= final output: ================
5—> ;
5—> 4 ; Velocity equation
2·f·t
#4: Vt = Vi + —————————
(Mi + Mt)
4—> code
Vt = (Vi + (2.0*f*t/(Mi + Mt)));
4—> ;
4—> 5 ; Position equation
t·(Vi + Vt)
#5: Pt = Pi + ———————————
2
5—> code
Pt = (Pi + (t*(Vi + Vt)/2.0));
5—> ;
5—> ; ================================================
5—> exit