Question

Mhm

Answer 1

\[\text{Total area} = X + Y \implies \frac{ 1 }{ 2 }t(\vec v_f- \vec v_i) +\vec v_i t\]

Answer 2

Where total area is displacement

Answer 3

\[\vec d = \frac{ \vec v_f t }{ 2 }- \frac{ \vec v_i t }{ 2 }+v_i t\]
\[\vec d = \frac{ \vec v_f t }{ 2 }+\frac{ \vec v_i t }{ 2 } = \left( \frac{ \vec v_f + \vec v_i }{ 2 } \right)t\]

\[\text{Therefore} ~ \vec d = \left( \frac{ \vec v_f + \vec v_i }{ 2 } \right)t\]

Answer 4

Ah, so now similarly can derive the other equations of uniform motion, using just the graphs :).

Answer 5

Using above being derived from