User:Narendra Sisodiya/mechanics

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Deriving the equations in vectors[edit]

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

Deriving v(t) = Ui + A (t - Ti)[edit]


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[edit]

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)[edit]


taking case for final velocity

eq ... (7)

or

eq ... (7)