Question

how to derive the formula of dynamics?

Answer 1

Which formula?

Answer 2

mv and mu bla bla bla...

Answer 3

which dynamics

Answer 4

You mean this? :-
Total Momentum before collision = Total momentum after collision
MU + mu = MV + mv - (1)
Total Kinetic energy before collision = Total Kinetic energy after collision
1/2MU^2 + 1/2mu^2 = 1/2 MV^2 + 1/2mv^2
canceling 1/2
MU^2 + mu^2 = MV^2 + mv^2 - (2)
Rearranging (2)
MU^2 - MV^2 = mv^2 - mu^2 - (3)
Rearranging (1)
MU-MV = mv - mu -(4)
(3)/(4)
(MU^2 - MV^2) / (MU-MV) = (mv^2 - mu^2) / (mv-mu)
(U^2 - V^2) / (U-V) = (v^2 - u^2) / (v-u)
((U - V)(U + V)) / (U - V) = ((v - u)(v + u)) / (v - u)
Further canceling,
U + V = v + u
OR
U - u = v - V
*Note that U > u and v < V

Answer 5

Sorry, but this: "mv and mu bla bla bla..." is too vague.

There is no such thing as A formula for dynamics.