Question

derrive the equation v=u+at

Answer 1

derivation of the equation v = u + at    
( please read the following steps continuously I just separated so that it would be easy for you to understand the terms )
consider a body is having initial velocity that is represented as "u"
that body is in uniform acceleration "a" 
after some time "t"
the body final velocity "v"

considering the definition  of the acceleration :
acceleration = change in velocity
                       --------------------------
                                  time

acceleration = final velocity - initial velocity 
                        ------------------------------------
                                       time

=> a = v-u
           -----
             t
=> (v-u) = at
=> v = u + at

hence the equation is derived.

hope so it is clear and understandable.

Answer 2

for IX class.
a=v-u/t
at=v-u
v=u+at