Question

What's the difference between V_x = v_x + a_xt
and
Vavg_x = v_x + 1/2a_xt?
you could only use them with constant acceleration but whats the difference?

Answer 1

the first equation you have written is the solution of differential equation dv/dt=a .
And the second equation you have written is the result that follows from the definition of average velocity for a uniformly accelerated motion.

vf=vi+at.....................(1)

where vf is the final speed
vi is the initial speed

average speed (for uniform as well as non uniform acceleration) is defined as

v_avg = total distance travelled / total time taken

for uniform acceleration

total distance travelled = (vf^2 - vi^2) / 2a
total time taken = (vf-vi) / a [from eqn 1]
Hence
v_avg = (vf+vi)/2

Eliminating vf by using eqn (1) we get

v_avg = vi + at/2