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

step inference rule input feed output step validity (as per SymPy)
1
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 3366703541
    \(a=\frac{v - v_0}{t}\)
 no validation is available for declarations
2
  • 111182: 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}.
  1. 3366703541
    \(a=\frac{v - v_0}{t}\)
  1. 7083390553
    \(t\)
  1. 4748157455
    \(a t=v - v_0\)
 valid
3
  • 111530: 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}.
  1. 4748157455
    \(a t=v - v_0\)
  1. 6417359412
    \(v_0\)
  1. 4798787814
    \(a t + v_0=v\)
 valid
4
  • 111268: 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}.
  1. 4798787814
    \(a t + v_0=v\)
  1. 3462972452
    \(v=v_0 + a t\)
 valid
5
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 3462972452
    \(v=v_0 + a t\)
 no validation is available for declarations
6
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 3411994811
    \(v_{\rm average}=\frac{d}{t}\)
 no validation is available for declarations
7
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 6175547907
    \(v_{\rm average}=\frac{v + v_0}{2}\)
 no validation is available for declarations
8
  • 111355: 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}.
  1. 3411994811
    \(v_{\rm average}=\frac{d}{t}\)
  1. 6175547907
    \(v_{\rm average}=\frac{v + v_0}{2}\)
  1. 9897284307
    \(\frac{d}{t}=\frac{v + v_0}{2}\)
 valid
9
  • 111182: 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}.
  1. 9897284307
    \(\frac{d}{t}=\frac{v + v_0}{2}\)
  1. 8865085668
    \(t\)
  1. 8706092970
    \(d=\left(\frac{v + v_0}{2}\right)t\)
 valid
10
  • 111634: 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}.
  1. 8706092970
    \(d=\left(\frac{v + v_0}{2}\right)t\)
  1. 3462972452
    \(v=v_0 + a t\)
  1. 7011114072
    \(d=\frac{(v_0 + a t) + v_0}{2} t\)
 LHS diff is pdg0001357 - pdg0001943 RHS diff is -pdg0001467**2*pdg0009140/2 - pdg0001467*pdg0005153 + pdg0001467*pdg0009140 + pdg0005153
11
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 7011114072
    \(d=\frac{(v_0 + a t) + v_0}{2} t\)
  1. 1265150401
    \(d=\frac{2 v_0 + a t}{2} t\)
 valid
12
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 1265150401
    \(d=\frac{2 v_0 + a t}{2} t\)
  1. 9658195023
    \(d=v_0 t + \frac{1}{2} a t^2\)
 valid
13
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 9658195023
    \(d=v_0 t + \frac{1}{2} a t^2\)
 no validation is available for declarations
14
  • 111483: 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}.
  1. 3462972452
    \(v=v_0 + a t\)
  1. 5799753649
    \(2\)
  1. 7215099603
    \(v^2=v_0^2 + 2 a t v_0 + a^2 t^2\)
 recognized infrule but not yet supported
15
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 7215099603
    \(v^2=v_0^2 + 2 a t v_0 + a^2 t^2\)
  1. 5144263777
    \(v^2=v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)\)
 invalid syntax (<string>, line 0)
16
  • 111634: 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}.
  1. 5144263777
    \(v^2=v_0^2 + 2 a \left( v_0 t +\frac{1}{2} a t^2 \right)\)
  1. 9658195023
    \(d=v_0 t + \frac{1}{2} a t^2\)
  1. 7939765107
    \(v^2=v_0^2 + 2 a d\)
 invalid syntax (<string>, line 0)
17
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 7939765107
    \(v^2=v_0^2 + 2 a d\)
 no validation is available for declarations
18
  • 111282: 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}.
  1. 3462972452
    \(v=v_0 + a t\)
  1. 6729698807
    \(v_0\)
  1. 9759901995
    \(v - v_0=a t\)
 valid
19
  • 111268: 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}.
  1. 9759901995
    \(v - v_0=a t\)
  1. 4748157455
    \(a t=v - v_0\)
 valid
20
  • 111975: 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}.
  1. 4748157455
    \(a t=v - v_0\)
  1. 2242144313
    \(a\)
  1. 1967582749
    \(t=\frac{v - v_0}{a}\)
 valid
21
  • 111634: 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}.
  1. 8706092970
    \(d=\left(\frac{v + v_0}{2}\right)t\)
  1. 1967582749
    \(t=\frac{v - v_0}{a}\)
  1. 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
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 5733721198
    \(d=\frac{1}{2} (v + v_0) \left( \frac{v - v_0}{a} \right)\)
  1. 5611024898
    \(d=\frac{1}{2 a} (v^2 - v_0^2)\)
 valid
23
  • 111182: 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}.
  1. 5611024898
    \(d=\frac{1}{2 a} (v^2 - v_0^2)\)
  1. 5542390646
    \(2 a\)
  1. 8269198922
    \(2 a d=v^2 - v_0^2\)
 valid
24
  • 111530: 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}.
  1. 8269198922
    \(2 a d=v^2 - v_0^2\)
  1. 9070454719
    \(v_0^2\)
  1. 4948763856
    \(2 a d + v_0^2=v^2\)
 valid
25
  • 111268: 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}.
  1. 4948763856
    \(2 a d + v_0^2=v^2\)
  1. 7939765107
    \(v^2=v_0^2 + 2 a d\)
 valid
26
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 8706092970
    \(d=\left(\frac{v + v_0}{2}\right)t\)
 no validation is available for declarations
27
  • 111282: 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}.
  1. 3462972452
    \(v=v_0 + a t\)
  1. 9645178657
    \(a t\)
  1. 6457044853
    \(v - a t=v_0\)
 valid
28
  • 111634: 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}.
  1. 9658195023
    \(d=v_0 t + \frac{1}{2} a t^2\)
  1. 6457044853
    \(v - a t=v_0\)
  1. 1259826355
    \(d=(v - a t) t + \frac{1}{2} a t^2\)
 LHS diff is pdg0001357 - pdg0001467*pdg0009140 - pdg0001943 RHS diff is -pdg0001357*pdg0001467 + pdg0001467**2*pdg0009140/2 + pdg0005153
29
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 1259826355
    \(d=(v - a t) t + \frac{1}{2} a t^2\)
  1. 4580545876
    \(d=v t - a t^2 + \frac{1}{2} a t^2\)
 valid
30
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 4580545876
    \(d=v t - a t^2 + \frac{1}{2} a t^2\)
  1. 6421241247
    \(d=v t - \frac{1}{2} a t^2\)
 valid
31
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 6421241247
    \(d=v t - \frac{1}{2} a t^2\)
 no validation is available for declarations


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