Question

Deriving Physics Equations?
My textbook is not clear and I need help with how they went from step 3 to 4.

Answer 1

Step 1: \[X = v _{i}t\]

Step 2: \[Y = \frac{ 1 }{ 2 }t(v _{f}-v _{i})\]

Step 3: \[X + Y = v _{i}t+(\frac{ v _{f} t }{ 2 }-\frac{ v _{i} t }{ 2 })\]

Step 4: \[d = (\frac{ v _{f}+v _{i} }{ 2 })t\]

Answer 2

I'm starting with step 3


\[X + Y = v _{i}t+(\frac{ v _{f} t }{ 2 }-\frac{ v _{i} t }{ 2 })\]


\[X + Y = \frac{2v _{i}t}{2}+(\frac{ v _{f} t }{ 2 }-\frac{ v _{i} t }{ 2 })\]


\[X + Y = \frac{2v _{i}t}{2}+\frac{ v _{f} t }{ 2 }-\frac{ v _{i} t }{ 2 }\]


\[X + Y = \frac{2v _{i}t}{2}-\frac{ v _{i} t }{ 2 }+\frac{ v _{f} t }{ 2 }\]


\[X + Y = \frac{2v _{i}t-v _{i} t}{2}+\frac{ v _{f} t }{ 2 }\]


\[X + Y = \frac{v _{i} t}{2}+\frac{ v _{f} t }{ 2 }\]


\[X + Y = \frac{v _{i} t+ v _{f} t }{ 2 }\]


\[X + Y = \frac{(v _{i} + v _{f}) t }{ 2 }\]


\[X + Y = \left(\frac{v _{i} + v _{f} }{ 2 }\right)t\]


\[d = \left(\frac{v _{i} + v _{f} }{ 2 }\right)t\]

Answer 3

thanks @jim_thompson5910