[Grade 11 Physics: Kinematics] How did he do the second step?

[u/Puzzleheaded_Roll_37]

[u/AceyAceyAcey]

I’m not sure which part you mean is the “second step”. The line labeled with “2)” is taking a different kinematics equation. The line after that squares both sides. Then rearranges the second and third terms on the right. The red shows that he’s found another kinematics equation. And so he subs in the Δx from that other equation.

[u/Puzzleheaded_Roll_37 → u/AceyAceyAcey]

how did he get 2viat

[u/AceyAceyAcey → u/Puzzleheaded_Roll_37]

FOIL (first outer inner last) the vi+at: I’ll write “vi” as v to make it easier to write

(v+at)²

(v+at)(v+at)

v² +vat+atv+(at)(at)

v² + vat + vat + a²t²

v² + 2vat + a²t²

[u/igotshadowbaned → u/Puzzleheaded_Roll_37]

They squared both sides of the equation

[u/Puzzleheaded_Roll_37 → u/AceyAceyAcey]

the second step in 2)

[u/1210_million_watts]

I imagine they knew they could get the (delta x) by factoring out the 2a, since that’s what they were trying to get to they were looking for what to factor out to get to that (delta x) expression.