Hi, most of the time I found incorrect equation of motion for classical mechanics with constant acceleration. So here are the correct equation in vector format with removing all assumptions.
Deriving the equations in vectors
- All constant are taken in capital letters
- All variable are given in small letter
Deriving v(t) = Ui + A (t - Ti)
so
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
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 t = Tf 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)
taking case for final velocity
![]() | eq ... (7) |
or
![]() | eq ... (7) |
Source Page : http://en.wikipedia.org/wiki/User:Narendra_Sisodiya/mechanics
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