Deriving the equations in vectors

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  • All constant are taken in capital letters
  • All variable are given in small letter

Deriving v(t) = Ui + A (t - Ti)

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so <br\>

 

for zero or constant acceleration A we have

 
 
 

we have one unknown K , we need to consider initial or final condition

  • Lets take initially we have  
 

ie

 
  eq ... (1)

If we take final condition in consideration then ie :  

  eq ... (2)

constant acceleration can be found using initial and final condition

  eq ... (3)

Deriving s(t) = Si + Ui(t-Ti) + (1/2)A (t - Ti)2

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now we have

 
 
 
 


 

for eliminating K we need either final or initial condition ie  

 
 
 
 
 
  eq ... (4)

If we would have taken final condition ie   then

  eq ... (5)

Taking   and putting eq (3) in eq (4) , we will get

 

Or

 
  eq ... (6)


Deriving |v(t)|2 = |Ui|2 + 2 A . (s(t)-S_i)

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taking case for final velocity

  eq ... (7)

or

  eq ... (7)