#2**+1 **

Here's the first part

v = u + at

Note that a = change in velocity / change in time

So...... change in velocity / change in time = (v - u ) / t

So we have that

v = u + at

v = u + [ ( v - u) / t ] * t

v = u + (v - u)

v = u + v - u

v = v

CPhill Mar 4, 2019

#5**+1 **

Second part

The total displacement, s, is the green area

Notice that the total shaded area of the bottom rectangle is u* t

And the area of the top rectange is (v - u)* t

But only half of this rectangle is shaded...so....the shaded area in the top rectangle is (1/2)(v - u) * t

So.....the displacement is

u * t + (1/2) ( v - u) *t =

u * t + (1/2)v*t - (1/2)u*t =

1/2 v* t + 1/2 u*t =

(1/2) ( u + v) * t = s

CPhill Mar 4, 2019