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Review equations of motion in 1D with constant acceleration - SUVAT (algebra)

abstract:
reference: https://en.wikipedia.org/wiki/Equations_of_motion

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3366703541 $a = \frac{v - v_0}{t}$	no validation is available for declarations
2	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	3366703541 $a = \frac{v - v_0}{t}$	7083390553 $t$	4748157455 $a t = v - v_0$	valid
3	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	4748157455 $a t = v - v_0$	6417359412 $v_0$	4798787814 $a t + v_0 = v$	valid
4	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	4798787814 $a t + v_0 = v$		3462972452 $v = v_0 + a t$	valid
5	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	3462972452 $v = v_0 + a t$			no validation is available for declarations
6	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3411994811 $v_{\rm average} = \frac{d}{t}$	no validation is available for declarations
7	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			6175547907 $v_{\rm average} = \frac{v + v_0}{2}$	no validation is available for declarations
8	0000111355: LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\ref{eq:#1} is equal to LHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	6175547907 $v_{\rm average} = \frac{v + v_0}{2}$ 3411994811 $v_{\rm average} = \frac{d}{t}$		9897284307 $\frac{d}{t} = \frac{v + v_0}{2}$	input diff is 0 diff is (pdg0001467(pdg0001357 + pdg0005153)/2 - pdg0001943)/pdg0001467 diff is (-pdg0001467(pdg0001357 + pdg0005153)/2 + pdg0001943)/pdg0001467
9	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	9897284307 $\frac{d}{t} = \frac{v + v_0}{2}$	8865085668 $t$	8706092970 $d = \left(\frac{v + v_0}{2}\right)t$	valid
10	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8706092970 $d = \left(\frac{v + v_0}{2}\right)t$ 3462972452 $v = v_0 + a t$		7011114072 $d = \frac{(v_0 + a t) + v_0}{2} t$	LHS diff is pdg0001357 - pdg0001943 RHS diff is -pdg0001467*2pdg0009140/2 - pdg0001467pdg0005153 + pdg0001467pdg0009140 + pdg0005153
11	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	7011114072 $d = \frac{(v_0 + a t) + v_0}{2} t$		1265150401 $d = \frac{2 v_0 + a t}{2} t$	valid
12	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1265150401 $d = \frac{2 v_0 + a t}{2} t$		9658195023 $d = v_0 t + \frac{1}{2} a t^2$	valid
13	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	9658195023 $d = v_0 t + \frac{1}{2} a t^2$			no validation is available for declarations
14	0000111483: raise both sides to power number of inputs: 1; feeds: 1; outputs: 1 Raise both sides of Eq.~\ref{eq:#2} to $#1$; yields Eq.~\ref{eq:#3}.	3462972452 $v = v_0 + a t$	5799753649 $2$	7215099603 $v^2 = v_0^2 + 2 a t v_0 + a^2 t^2$	recognized infrule but not yet supported
15	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	7215099603 $v^2 = v_0^2 + 2 a t v_0 + a^2 t^2$		5144263777 $v^2 = v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)$	Not evaluated due to missing term in SymPy
16	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	9658195023 $d = v_0 t + \frac{1}{2} a t^2$ 5144263777 $v^2 = v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)$		7939765107 $v^2 = v_0^2 + 2 a d$	Not evaluated due to missing term in SymPy
17	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7939765107 $v^2 = v_0^2 + 2 a d$			no validation is available for declarations
18	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3462972452 $v = v_0 + a t$	6729698807 $v_0$	9759901995 $v - v_0 = a t$	valid
19	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	9759901995 $v - v_0 = a t$		4748157455 $a t = v - v_0$	valid
20	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4748157455 $a t = v - v_0$	2242144313 $a$	1967582749 $t = \frac{v - v_0}{a}$	valid
21	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8706092970 $d = \left(\frac{v + v_0}{2}\right)t$ 1967582749 $t = \frac{v - v_0}{a}$		5733721198 $d = \frac{1}{2} (v + v_0) \left( \frac{v - v_0}{a} \right)$	LHS diff is pdg0001467 - pdg0001943 RHS diff is (pdg0001357 - pdg0005153 - (pdg0001357 - pdg0005153)*(pdg0001357 + pdg0005153)/2)/pdg0009140
22	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	5733721198 $d = \frac{1}{2} (v + v_0) \left( \frac{v - v_0}{a} \right)$		5611024898 $d = \frac{1}{2 a} (v^2 - v_0^2)$	valid
23	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	5611024898 $d = \frac{1}{2 a} (v^2 - v_0^2)$	5542390646 $2 a$	8269198922 $2 a d = v^2 - v_0^2$	valid
24	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8269198922 $2 a d = v^2 - v_0^2$	9070454719 $v_0^2$	4948763856 $2 a d + v_0^2 = v^2$	valid
25	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	4948763856 $2 a d + v_0^2 = v^2$		7939765107 $v^2 = v_0^2 + 2 a d$	valid
26	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	8706092970 $d = \left(\frac{v + v_0}{2}\right)t$			no validation is available for declarations
27	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3462972452 $v = v_0 + a t$	9645178657 $a t$	6457044853 $v - a t = v_0$	valid
28	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	9658195023 $d = v_0 t + \frac{1}{2} a t^2$ 6457044853 $v - a t = v_0$		1259826355 $d = (v - a t) t + \frac{1}{2} a t^2$	LHS diff is pdg0001357 - pdg0001467pdg0009140 - pdg0001943 RHS diff is -pdg0001357pdg0001467 + pdg0001467*2pdg0009140/2 + pdg0005153
29	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1259826355 $d = (v - a t) t + \frac{1}{2} a t^2$		4580545876 $d = v t - a t^2 + \frac{1}{2} a t^2$	valid
30	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	4580545876 $d = v t - a t^2 + \frac{1}{2} a t^2$		6421241247 $d = v t - \frac{1}{2} a t^2$	valid
31	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	6421241247 $d = v t - \frac{1}{2} a t^2$			no validation is available for declarations

Symbols used in equations of motion in 1D with constant acceleration - SUVAT (algebra)

0000009140: $ a $
0000001943: $ d $
0000001467: $ t $
0000001357: $ v $
0000005153: $ v_0 $
0000006709: $ v_{\rm average} $

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0.007 seconds for pdg_app/to_review_derivation 435b5c25-e825-4cef-afe6-46d7275e6424
0.015 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.003 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_ID1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUT1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.002 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEED1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.002 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUT1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.002 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_step1bcdf6ea-acb1-4ede-a170-722ad13f8f81
0.004 seconds for pdg_app/ 435b5c25-e825-4cef-afe6-46d7275e6424

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3366703541 \(a = \frac{v - v_0}{t}\)	no validation is available for declarations
2	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	3366703541 \(a = \frac{v - v_0}{t}\)	7083390553 \(t\)	4748157455 \(a t = v - v_0\)	valid
3	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	4748157455 \(a t = v - v_0\)	6417359412 \(v_0\)	4798787814 \(a t + v_0 = v\)	valid
4	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	4798787814 \(a t + v_0 = v\)		3462972452 \(v = v_0 + a t\)	valid
5	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	3462972452 \(v = v_0 + a t\)			no validation is available for declarations
6	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3411994811 \(v_{\rm average} = \frac{d}{t}\)	no validation is available for declarations
7	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			6175547907 \(v_{\rm average} = \frac{v + v_0}{2}\)	no validation is available for declarations
8	0000111355: LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\ref{eq:#1} is equal to LHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	6175547907 \(v_{\rm average} = \frac{v + v_0}{2}\) 3411994811 \(v_{\rm average} = \frac{d}{t}\)		9897284307 \(\frac{d}{t} = \frac{v + v_0}{2}\)	input diff is 0 diff is (pdg0001467(pdg0001357 + pdg0005153)/2 - pdg0001943)/pdg0001467 diff is (-pdg0001467(pdg0001357 + pdg0005153)/2 + pdg0001943)/pdg0001467
9	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	9897284307 \(\frac{d}{t} = \frac{v + v_0}{2}\)	8865085668 \(t\)	8706092970 \(d = \left(\frac{v + v_0}{2}\right)t\)	valid
10	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8706092970 \(d = \left(\frac{v + v_0}{2}\right)t\) 3462972452 \(v = v_0 + a t\)		7011114072 \(d = \frac{(v_0 + a t) + v_0}{2} t\)	LHS diff is pdg0001357 - pdg0001943 RHS diff is -pdg0001467*2pdg0009140/2 - pdg0001467pdg0005153 + pdg0001467pdg0009140 + pdg0005153
11	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	7011114072 \(d = \frac{(v_0 + a t) + v_0}{2} t\)		1265150401 \(d = \frac{2 v_0 + a t}{2} t\)	valid
12	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1265150401 \(d = \frac{2 v_0 + a t}{2} t\)		9658195023 \(d = v_0 t + \frac{1}{2} a t^2\)	valid
13	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	9658195023 \(d = v_0 t + \frac{1}{2} a t^2\)			no validation is available for declarations
14	0000111483: raise both sides to power number of inputs: 1; feeds: 1; outputs: 1 Raise both sides of Eq.~\ref{eq:#2} to $#1$; yields Eq.~\ref{eq:#3}.	3462972452 \(v = v_0 + a t\)	5799753649 \(2\)	7215099603 \(v^2 = v_0^2 + 2 a t v_0 + a^2 t^2\)	recognized infrule but not yet supported
15	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	7215099603 \(v^2 = v_0^2 + 2 a t v_0 + a^2 t^2\)		5144263777 \(v^2 = v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)\)	Not evaluated due to missing term in SymPy
16	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	9658195023 \(d = v_0 t + \frac{1}{2} a t^2\) 5144263777 \(v^2 = v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)\)		7939765107 \(v^2 = v_0^2 + 2 a d\)	Not evaluated due to missing term in SymPy
17	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	7939765107 \(v^2 = v_0^2 + 2 a d\)			no validation is available for declarations
18	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3462972452 \(v = v_0 + a t\)	6729698807 \(v_0\)	9759901995 \(v - v_0 = a t\)	valid
19	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	9759901995 \(v - v_0 = a t\)		4748157455 \(a t = v - v_0\)	valid
20	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4748157455 \(a t = v - v_0\)	2242144313 \(a\)	1967582749 \(t = \frac{v - v_0}{a}\)	valid
21	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8706092970 \(d = \left(\frac{v + v_0}{2}\right)t\) 1967582749 \(t = \frac{v - v_0}{a}\)		5733721198 \(d = \frac{1}{2} (v + v_0) \left( \frac{v - v_0}{a} \right)\)	LHS diff is pdg0001467 - pdg0001943 RHS diff is (pdg0001357 - pdg0005153 - (pdg0001357 - pdg0005153)*(pdg0001357 + pdg0005153)/2)/pdg0009140
22	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	5733721198 \(d = \frac{1}{2} (v + v_0) \left( \frac{v - v_0}{a} \right)\)		5611024898 \(d = \frac{1}{2 a} (v^2 - v_0^2)\)	valid
23	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	5611024898 \(d = \frac{1}{2 a} (v^2 - v_0^2)\)	5542390646 \(2 a\)	8269198922 \(2 a d = v^2 - v_0^2\)	valid
24	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8269198922 \(2 a d = v^2 - v_0^2\)	9070454719 \(v_0^2\)	4948763856 \(2 a d + v_0^2 = v^2\)	valid
25	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	4948763856 \(2 a d + v_0^2 = v^2\)		7939765107 \(v^2 = v_0^2 + 2 a d\)	valid
26	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	8706092970 \(d = \left(\frac{v + v_0}{2}\right)t\)			no validation is available for declarations
27	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3462972452 \(v = v_0 + a t\)	9645178657 \(a t\)	6457044853 \(v - a t = v_0\)	valid
28	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	9658195023 \(d = v_0 t + \frac{1}{2} a t^2\) 6457044853 \(v - a t = v_0\)		1259826355 \(d = (v - a t) t + \frac{1}{2} a t^2\)	LHS diff is pdg0001357 - pdg0001467pdg0009140 - pdg0001943 RHS diff is -pdg0001357pdg0001467 + pdg0001467*2pdg0009140/2 + pdg0005153
29	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1259826355 \(d = (v - a t) t + \frac{1}{2} a t^2\)		4580545876 \(d = v t - a t^2 + \frac{1}{2} a t^2\)	valid
30	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	4580545876 \(d = v t - a t^2 + \frac{1}{2} a t^2\)		6421241247 \(d = v t - \frac{1}{2} a t^2\)	valid
31	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	6421241247 \(d = v t - \frac{1}{2} a t^2\)			no validation is available for declarations