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:
Instructions:

  1. Store any 3 of the following:
  2. Clear the 2 unknowns: If t is unknown, 0 STO 0, etc.
  3. Calculate the unknowns A
  4. 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
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 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
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 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 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 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 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