Is this a valid Kinematics Equation?

[yosimba2000]

a = dv/dt
a = (d/dt)(dx/dt)
dv/dt = (d/dt)(dx/dt)
dv = dx/dt
dx = dvdt
Xf - Xi = (tf-t0)*dv

Is this a valid equation? It doesn't seem right to me since if velocity change is 0, then dv = 0, meaning your change in position is 0. That shouldn't be right, as even though your velocity change is 0, you still have velocity meaning you are moving. But the math seems like it works out.

 

[Orodruin]

dv/dt = (d/dt)(dx/dt)
dv = dx/dt

This step is wrong. Integrating both sides gives $v = dx/dt$ which is the definition of $v$.

 

[yosimba2000]

Oh, right! I should have read dv/dt as (d/dt)(v).