Equations of Motion
Description
This program provides an interchangeable solution between displacement, final velocity, accelaration, time and initial velocity for an object that undergoes constand acceleration. Given any three known parameters the two unknowns will be calculated. The motion must be linear.
Equations:
x = t(v + v0)/2
x = vt - 1/2at2
x = (v2 - v02)/2a
x = v0t + 1/2at2
v = v0 + at
where:
x = displacement
v = final velocity
a = accelerations
t = time
v0 = initial velocity
Remarks:
- Any consistent set of units may be used
- Displacement, acceleration, and velocity should be considered signed (vector) quantities. For example: if initial velocity and acceleration are in opposite directions, one should be positive and the other negative.
- All equations assume initial displacement, x0, equals zero.
Instructions:
- Store any 3 of the following:
- Time, t, if known STO 0
- Displacement, x, if known STO 1,
- Final velocity, v, if known STO 2
- Acceleration, a, if known STO 3
- Initial velocity, v0, if known STO I
- Clear the 2 unknowns: If t is unknown, 0 STO 0, etc.
- Calculate the unknowns A
- Recall the desired value: for t press RCL 0, etc.
Example 1:
An automobile accelerates for 4 seconds from a speed of 35 mph and covers a distance of 264 feet. What is the acceleration in ft/sec2? If the acceleration continous to be constant, what distance is covered in the next second?
264 STO 1
35 ENTER
5280 ×
3600 ÷ STO I → 51.3333 (v0, ft/sec)
4 STO 0
0 STO 2
STO 3 A
RCL 3 → 7.3333 (a, ft/sec2)
5 STO 0
0 STO 1
STO 2 A
RCL 1 → 348.3333 (x(t+1), ft)
264 – → 84.3333 (x(t+1) - x(t), ft)
Program Resources
Labels
Name |
Description |
|
Name |
Description |
|
A |
Caculate the unknowns |
|
5 |
# - internal use - |
|
0 |
# - internal use - |
|
6 |
# - internal use - |
|
1 |
# - internal use - |
|
7 |
# - internal use - |
|
2 |
# - internal use - |
|
8 |
# - internal use - |
|
3 |
# - internal use - |
|
9 |
# - internal use - |
|
Storage Registers
Name |
Description |
|
0 |
Time t |
|
1 |
Displacement x |
|
2 |
Velocity v |
|
3 |
Acceleration a |
|
I |
Initial velocity v0 |
|
Program
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
000 |
|
|
|
061 |
42,21, 1 |
f LBL 1 |
|
122 |
45 25 |
RCL I |
|
001 |
42,21,11 |
f LBL A |
|
062 |
45 2 |
RCL 2 |
|
123 |
43 11 |
g x² |
|
002 |
45 1 |
RCL 1 |
|
063 |
43,30, 0 |
g TEST x≠0 |
|
124 |
30 |
− |
|
003 |
43,30, 0 |
g TEST x≠0 |
|
064 |
22 3 |
GTO 3 |
|
125 |
45 1 |
RCL 1 |
|
004 |
22 1 |
GTO 1 |
|
065 |
45 3 |
RCL 3 |
|
126 |
10 |
÷ |
|
005 |
45 2 |
RCL 2 |
|
066 |
43,30, 0 |
g TEST x≠0 |
|
127 |
2 |
2 |
|
006 |
43,30, 0 |
g TEST x≠0 |
|
067 |
22 0 |
GTO 0 |
|
128 |
10 |
÷ |
|
007 |
22 0 |
GTO 0 |
|
068 |
45 1 |
RCL 1 |
|
129 |
2 |
2 |
|
008 |
45 25 |
RCL I |
|
069 |
45 0 |
RCL 0 |
|
130 |
10 |
÷ |
|
009 |
45 0 |
RCL 0 |
|
070 |
10 |
÷ |
|
131 |
44 3 |
STO 3 |
|
010 |
20 |
× |
|
071 |
2 |
2 |
|
132 |
42,21, 5 |
f LBL 5 |
|
011 |
45 3 |
RCL 3 |
|
072 |
20 |
× |
|
133 |
45 25 |
RCL I |
|
012 |
45 0 |
RCL 0 |
|
073 |
45 25 |
RCL I |
|
134 |
40 |
+ |
|
013 |
43 11 |
g x² |
|
074 |
30 |
− |
|
135 |
10 |
÷ |
|
014 |
20 |
× |
|
075 |
44 2 |
STO 2 |
|
136 |
2 |
2 |
|
015 |
2 |
2 |
|
076 |
22 7 |
GTO 7 |
|
137 |
20 |
× |
|
016 |
10 |
÷ |
|
077 |
42,21, 0 |
f LBL 0 |
|
138 |
44 0 |
STO 0 |
|
017 |
40 |
+ |
|
078 |
45 0 |
RCL 0 |
|
139 |
43 32 |
g RTN |
|
018 |
44 1 |
STO 1 |
|
079 |
43,30, 0 |
g TEST x≠0 |
|
140 |
42,21, 6 |
f LBL 6 |
|
019 |
22 2 |
GTO 2 |
|
080 |
22 2 |
GTO 2 |
|
141 |
45 2 |
RCL 2 |
|
020 |
42,21, 0 |
f LBL 0 |
|
081 |
45 1 |
RCL 1 |
|
142 |
43 11 |
g x² |
|
021 |
45 3 |
RCL 3 |
|
082 |
45 3 |
RCL 3 |
|
143 |
45 1 |
RCL 1 |
|
022 |
43,30, 0 |
g TEST x≠0 |
|
083 |
20 |
× |
|
144 |
45 3 |
RCL 3 |
|
023 |
22 0 |
GTO 0 |
|
084 |
2 |
2 |
|
145 |
20 |
× |
|
024 |
45 25 |
RCL I |
|
085 |
20 |
× |
|
146 |
2 |
2 |
|
025 |
45 2 |
RCL 2 |
|
086 |
45 25 |
RCL I |
|
147 |
20 |
× |
|
026 |
40 |
+ |
|
087 |
43 11 |
g x² |
|
148 |
30 |
− |
|
027 |
2 |
2 |
|
088 |
40 |
+ |
|
149 |
11 |
√x̅ |
|
028 |
10 |
÷ |
|
089 |
11 |
√x̅ |
|
150 |
45 1 |
RCL 1 |
|
029 |
45 0 |
RCL 0 |
|
090 |
45 1 |
RCL 1 |
|
151 |
36 |
ENTER |
|
030 |
20 |
× |
|
091 |
36 |
ENTER |
|
152 |
43 16 |
g ABS |
|
031 |
44 1 |
STO 1 |
|
092 |
43 16 |
g ABS |
|
153 |
10 |
÷ |
|
032 |
22 9 |
GTO 9 |
|
093 |
10 |
÷ |
|
154 |
16 |
CHS |
|
033 |
42,21, 0 |
f LBL 0 |
|
094 |
20 |
× |
|
155 |
20 |
× |
|
034 |
45 0 |
RCL 0 |
|
095 |
44 2 |
STO 2 |
|
156 |
45 2 |
RCL 2 |
|
035 |
43,30, 0 |
g TEST x≠0 |
|
096 |
22 5 |
GTO 5 |
|
157 |
40 |
+ |
|
036 |
22 0 |
GTO 0 |
|
097 |
42,21, 2 |
f LBL 2 |
|
158 |
45 3 |
RCL 3 |
|
037 |
45 2 |
RCL 2 |
|
098 |
45 1 |
RCL 1 |
|
159 |
10 |
÷ |
|
038 |
43 11 |
g x² |
|
099 |
45 0 |
RCL 0 |
|
160 |
44 0 |
STO 0 |
|
039 |
45 25 |
RCL I |
|
100 |
10 |
÷ |
|
161 |
43 32 |
g RTN |
|
040 |
43 11 |
g x² |
|
101 |
45 3 |
RCL 3 |
|
162 |
42,21, 7 |
f LBL 7 |
|
041 |
30 |
− |
|
102 |
45 0 |
RCL 0 |
|
163 |
45 2 |
RCL 2 |
|
042 |
45 3 |
RCL 3 |
|
103 |
20 |
× |
|
164 |
45 1 |
RCL 1 |
|
043 |
2 |
2 |
|
104 |
2 |
2 |
|
165 |
45 0 |
RCL 0 |
|
044 |
20 |
× |
|
105 |
10 |
÷ |
|
166 |
10 |
÷ |
|
045 |
10 |
÷ |
|
106 |
40 |
+ |
|
167 |
30 |
− |
|
046 |
44 1 |
STO 1 |
|
107 |
44 2 |
STO 2 |
|
168 |
45 0 |
RCL 0 |
|
047 |
22 5 |
GTO 5 |
|
108 |
22 8 |
GTO 8 |
|
169 |
10 |
÷ |
|
048 |
42,21, 0 |
f LBL 0 |
|
109 |
42,21, 3 |
f LBL 3 |
|
170 |
2 |
2 |
|
049 |
45 2 |
RCL 2 |
|
110 |
45 3 |
RCL 3 |
|
171 |
20 |
× |
|
050 |
45 0 |
RCL 0 |
|
111 |
43 20 |
g x=0 |
|
172 |
44 3 |
STO 3 |
|
051 |
20 |
× |
|
112 |
22 0 |
GTO 0 |
|
173 |
42,21, 8 |
f LBL 8 |
|
052 |
45 3 |
RCL 3 |
|
113 |
32 6 |
GSB 6 |
|
174 |
45 2 |
RCL 2 |
|
053 |
45 0 |
RCL 0 |
|
114 |
22 8 |
GTO 8 |
|
175 |
45 3 |
RCL 3 |
|
054 |
43 11 |
g x² |
|
115 |
42,21, 0 |
f LBL 0 |
|
176 |
45 0 |
RCL 0 |
|
055 |
20 |
× |
|
116 |
45 0 |
RCL 0 |
|
177 |
20 |
× |
|
056 |
2 |
2 |
|
117 |
43,30, 0 |
g TEST x≠0 |
|
178 |
30 |
− |
|
057 |
10 |
÷ |
|
118 |
22 7 |
GTO 7 |
|
179 |
44 25 |
STO I |
|
058 |
30 |
− |
|
119 |
42,21, 9 |
f LBL 9 |
|
180 |
43 32 |
g RTN |
|
059 |
44 1 |
STO 1 |
|
120 |
45 2 |
RCL 2 |
|
|
|
|
|
060 |
22 8 |
GTO 8 |
|
121 |
43 11 |
g x² |
|
|
|
|
|