Question

where symbols of v=u+at have there usual meaning

Answer 1

Let u be the initial velocity
v = Final Velocity

In the Velocity time graph , the particle increases it's speed from u in t = 0 to v in t = t'

So , we can write expression for acceleration as
a = v - u/ t - 0
a = (v - u)/t
at = v - u
v = u + at

Hope This Helps You!

Answer 2

I think your question is -----> Derive v = u + at , where symbols of v= u + at has their usual meaning.

solution :- Let a particle moves with velocity u , and after time t particle gains v velocity. it is clear in attachment.
Now, we have to proof : v = u + at
We know, slope of velocity - time graph = acceleration
now, slope of AB = ( v - u)/t = acceleration ( let a )
v - u = at
v = u + at
Hence proved