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Programs

Physics Programs

Uniform Acceleration Solution

Summary Description

Programs:

UNIFACCE

Version:

1.0, 22 January 2006

Description:

The UNIFACCE program computes the factors of a body undergoing uniform acceleration that can be deduced from a given set of factors.

Compatibility:

Is compatible CFX-9850G

Compatible with CFX-9850G

Is compatible FX-7400G

Compatible with FX-7400G

Detailed Description

The UNIFACCE program computes the unknown quantities that can be deduced from known quantities using the following equations of uniformly accelerated motion:

Equations of uniformly accelerated motion

The subscripts 0 and f indicate initial and final value of the quantity, respectively; the operator Δ represents the change in the quantity; and s indicates distance, v indicates velocity, a indicates acceleration, and t indicates time.

There are combinations of values for which there is no solution for some or all remaining quantities, or for which there is not a unique solution for some or all remaining quantities. In these circumstances, the program will issue a diagnostic or fail to produce values for some quantities. However, if there are two possible solutions for time, based on the quadratic equation, the program will produce both solutions. The smaller positive value, if there is one, will be identified as “the” solution for t, and the other will be identified as an “alternate” solution for t.

Usage

Enter the UNIFACCE program into the calculator, using either the calculator data cable or entering the program directly.

Choose a system of measurement (mKs, cgs, English, etc.), and convert all known values into this system. The results in the solution will also be expressed in this system.

Run the program.

Screen shot The program will display the prompt “1:A 2:Vini 3:Vfin 4:DelV 5:DelT 6:Sini 7:Sfin 8:DelS 0:Done?” and pause for you to input a code. This menu is shown in the screen shot to the right. These codes refer to: a, the acceleration (here called A, code 1); v0, the initial velocity (here called Vini, code 2); vf, the final velocity (here called Vfin, code 3); Δv, the change in velocity (here called DelV, code 4); Δt, the amount of time over which the uniform acceleration is applied (here called DelT, code 5); s0, the initial displacement or distance (here called Sini, code 6); sf, the final displacement or distance (here called Sfin, code 6); and Δs, the change in displacement or distance (here called DelS, code 7).

Screen shot You enter each known factor by first entering the appropriate code (1 through 8), then entering the factor’s value. The program displays the name of the factor after you enter the factor’s code, to help ensure the correct factor is entered. This two-step process of identifying the data to be entered, then entering the data, is indicated in the screen shot to the right.

If you enter an incorrect value for a factor, you can enter the factor again with the correct value. The most recently entered factor value is the value that is used. If you enter an incorrect factor code, you must restart the program. There is no way to “erase” a factor once it has been entered.

Screen shot When you have entered all the known factor values, use the code 0 to indicate that entry of the factor values is complete. The program will then compute and display the factor values that were not entered and can be deduced from the factors that were entered. The display of values is shown in the screen shot to the right.

Screen shot The program displays the message “Done” when it has displayed all the factors which can be determined from the factors you entered. This may occur without the display of any factors which were deduced, if the information you entered was insufficient to deduce any factors. This message is shown in the screen shot to the left.

Program

Source Code

The program is available in a ZIP file, or may be entered as shown below. Remember that this program is copyrighted; see the copyright issues page for limitations on redistribution.

Program UNIFACCE (1638 bytes):

'UNIFACCE 1.0End of line operator
0→A~SEnd of line operator
DoEnd of line operator
ClrTextEnd of line operator
"1:A 5:DelT2:Vini 6:Sini3:Vfin 7:Sfin4:DelV 8:DelS0:Done"?→AEnd of line operator
If A=1End of line operator
Then 1→BEnd of line operator
"A"?→CEnd of line operator
IfEndEnd of line operator
If A=2End of line operator
Then 1→DEnd of line operator
"Vini"?→EEnd of line operator
IfEndEnd of line operator
If A=3End of line operator
Then 1→FEnd of line operator
"Vfin"?→GEnd of line operator
IfEndEnd of line operator
If A=4End of line operator
Then 1→HEnd of line operator
"DelV"?→IEnd of line operator
IfEndEnd of line operator
If A=5End of line operator
Then 1→JEnd of line operator
"DelT"?→KEnd of line operator
IfEndEnd of line operator
If A=6End of line operator
Then 1→LEnd of line operator
"Sini"?→MEnd of line operator
IfEndEnd of line operator
If A=7End of line operator
Then 1→NEnd of line operator
"Sfin"?→OEnd of line operator
IfEndEnd of line operator
If A=8End of line operator
Then 1→PEnd of line operator
"DelS"?→QEnd of line operator
IfEndEnd of line operator
LpWhile A≠0End of line operator
DoEnd of line operator
0→AEnd of line operator
If B(H=0)JEnd of line operator
Then 1→AEnd of line operator
2→HEnd of line operator
CK→IEnd of line operator
IfEndEnd of line operator
If BH(J=0)End of line operator
Then If C≠0End of line operator
Then 1→AEnd of line operator
2→JEnd of line operator
I÷C→KEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If (B=0)HJEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→BEnd of line operator
I÷K→CEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If DF(H=0)End of line operator
Then 1→AEnd of line operator
2→HEnd of line operator
G-E→IEnd of line operator
IfEndEnd of line operator
If D(F=0)HEnd of line operator
Then 1→AEnd of line operator
2→FEnd of line operator
E+I→GEnd of line operator
IfEndEnd of line operator
If (D=0)FHEnd of line operator
Then 1→AEnd of line operator
2→DEnd of line operator
G-I→EEnd of line operator
IfEndEnd of line operator
If DFJ(P=0)End of line operator
Then 1→AEnd of line operator
2→PEnd of line operator
(E+G)K÷2→QEnd of line operator
IfEndEnd of line operator
If DF(J=0)PEnd of line operator
Then If E≠(-)GEnd of line operator
Then 1→AEnd of line operator
2→JEnd of line operator
2Q÷(E+G)→KEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If D(F=0)JPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→FEnd of line operator
2Q÷K-E→GEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If (D=0)FJPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→DEnd of line operator
2Q÷K-G→EEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If LN(P=0)End of line operator
Then 1→AEnd of line operator
2→PEnd of line operator
O-M→QEnd of line operator
IfEndEnd of line operator
If (L=0)NPEnd of line operator
Then 1→AEnd of line operator
2→LEnd of line operator
O-Q→MEnd of line operator
IfEndEnd of line operator
If L(N=0)PEnd of line operator
Then 1→AEnd of line operator
2→NEnd of line operator
M+Q→OEnd of line operator
IfEndEnd of line operator
If BDJ(P=0)End of line operator
Then 1→AEnd of line operator
2→PEnd of line operator
.5CK2+EK→QEnd of line operator
IfEndEnd of line operator
If B(D=0)JPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→DEnd of line operator
(Q-.5CK2)÷K→EEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If (B=0)DJPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→BEnd of line operator
2(Q-EK)÷K2→CEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If BD(J=0)PEnd of line operator
Then If C=0End of line operator
Then 1→AEnd of line operator
2→JEnd of line operator
Q÷E→KEnd of line operator
Else E2+2CQ→SEnd of line operator
If S<0End of line operator
Then "No real T"End of line operator
Else ((-)E-√S)÷C→REnd of line operator
((-)E+√S)÷C→SEnd of line operator
If R>SEnd of line operator
Then S→AEnd of line operator
R→SEnd of line operator
A→REnd of line operator
IfEndEnd of line operator
If R>0End of line operator
Then R→KEnd of line operator
Else S→KEnd of line operator
R→SEnd of line operator
IfEndEnd of line operator
1→AEnd of line operator
2→JEnd of line operator
2→REnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If BFJ(P=0)End of line operator
Then 1→AEnd of line operator
2→PEnd of line operator
(-).5CK2+GK→QEnd of line operator
IfEndEnd of line operator
If BF(J=0)PEnd of line operator
Then If C=0End of line operator
Then 1→AEnd of line operator
2→JEnd of line operator
Q÷G→KEnd of line operator
Else G2-2CQ→REnd of line operator
If R<0End of line operator
Then "No real T"End of line operator
Else (G+√R)÷C→SEnd of line operator
(G-√R)÷C→REnd of line operator
If R>SEnd of line operator
Then R→AEnd of line operator
S→REnd of line operator
A→SEnd of line operator
IfEndEnd of line operator
If R>0End of line operator
Then R→KEnd of line operator
Else S→KEnd of line operator
R→SEnd of line operator
IfEndEnd of line operator
1→AEnd of line operator
2→JEnd of line operator
2→REnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If B(F=0)JPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→FEnd of line operator
(Q+.5CK2)÷K→GEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If (B=0)FJPEnd of line operator
Then If K≠0End of line operator
Then 1→AEnd of line operator
2→BEnd of line operator
(GK-O)÷K2→CEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If (B=0)DFPEnd of line operator
Then If Q≠0End of line operator
Then 1→AEnd of line operator
2→BEnd of line operator
.5(G2-E2)÷Q→CEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
If BDF(P=0)End of line operator
Then If C≠0End of line operator
Then 1→AEnd of line operator
2→PEnd of line operator
.5(G2-E2)÷C→QEnd of line operator
IfEndEnd of line operator
IfEndEnd of line operator
LpWhile A≠0End of line operator
If B>1End of line operator
Then "A"End of line operator
CDisplay operator
IfEndEnd of line operator
If D>1End of line operator
Then "Vini"End of line operator
EDisplay operator
IfEndEnd of line operator
If F>1End of line operator
Then "Vfin"End of line operator
GDisplay operator
IfEndEnd of line operator
If H>1End of line operator
Then "DelV"End of line operator
IDisplay operator
IfEndEnd of line operator
If J>1End of line operator
Then "DelT"End of line operator
KDisplay operator
IfEndEnd of line operator
If R>1End of line operator
Then "T2"End of line operator
SDisplay operator
IfEndEnd of line operator
If L>1End of line operator
Then "Sini"End of line operator
MDisplay operator
IfEndEnd of line operator
If N>1End of line operator
Then "Sfin"End of line operator
ODisplay operator
IfEndEnd of line operator
If P>1End of line operator
Then "DelS"End of line operator
QDisplay operator
IfEndEnd of line operator
"Done"

Programming Notes

The program tests for multi-variable conditions by using arithmetic. The values used are 0 for false, and non-zero for true; note that the calculator’s various control constructs use the same convention. This permits multiplication to be used as an equivalent to logical and, addition to be used as an equivalent to logical or, and testing for not equal to 0 to be used as an equivalent to logical not.

Each factor is kept as a pair of values: the first value indicates whether the factor is known and, if known, how it is known, while the second value indicates the factor’s value. The first value is 0 to indicate the factor is not known, 1 to indicate the factor was entered by the user, and 2 to indicate the factor was computed by the program. Only factors computed by the program are displayed.

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Copyright © 2006 Brian Hetrick
Page last updated 22 January 2006.

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