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Notes for this derivation:
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Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

1  declare initial expr 



no validation is available for declarations 
1590774089:

1590774089:


2  integrate 



no check performed 
1590774089:
5542528160: 
1590774089:
5542528160: 

3  evaluate definite integral 



valid 
5542528160:
3512166162: 
5542528160:
3512166162: 

4  substitute LHS of expr 1 into expr 2 



LHS diff is pdg4202  pdg6789 RHS diff is pdg5156*pdg9140*(1  pdg4037) 
3512166162:
5345738321: 8953094349: 
3512166162:
5345738321: 8953094349: 

5  change three variables in expr 



LHS diff is pdg1943  pdg4037 RHS diff is (pdg2473**2  pdg5153**2)/(2*pdg9140) 
5611024898:
3253234559: 
5611024898:
3253234559: 

6  substitute LHS of expr 1 into expr 2 



valid 
3253234559:
8953094349: 9413699705: 
3253234559:
8953094349: 9413699705: 

7  simplify 



valid 
9413699705:
4811121942: 
9413699705:
4811121942: 

8  substitute LHS of two expressions into expr 



failed 
7676652285:
4928007622: 4811121942: 3360172339: dimensions are consistent 
7676652285:
4928007622: 4811121942: 3360172339: N/A 

9  declare final expr 



no validation is available for declarations 
3360172339:
dimensions are consistent 
3360172339:
N/A 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

9398  variable 
dW
\(dW\) 
real 

differential work 

2  
6789  variable 
W
\(W\) 
real 

work  10  
9140  variable 
a
\(a\) 
['real'] 

acceleration  29  
4770  variable 
v_2
\(v_2\) 
real 

velocity 2  14  
1955  variable 
KE_1
\(KE_1\) 
real 

kinetic energy  17  
1357  variable 
v
\(v\) 
['real'] 

velocity 

80  
4037  variable 
x
\(x\) 
['real'] 

position 

47  
2473  variable 
v_1
\(v_1\) 
real 

velocity 1  14  
1943  variable 
d
\(d\) 
['real'] 

displacement  25  
5153  variable 
v_0
\(v_0\) 
['real'] 

initial velocity  44  
1352  variable 
KE_2
\(KE_2\) 
real 

kinetic energy  14  
4202  variable 
F
\(F\) 
['real'] 

force  21  
9199  variable 
dx
\(dx\) 
['real'] 

15  
5156  variable 
m
\(m\) 
['real'] 

mass  49 