Question

Derive an expression relating acceleration initial velocity final velocity and time

Answer 1

We know

$\frac{d(v)}{dt}=a$

Then we can rewrite this and integrate lhs wrt v and rhs wrt t:

$\int\limits^v_u {} \, dv = \int\limits^t_0 {a} \, dt \\v-u=at\\v=u+at$