Step-by-step explanation:
Your answers to 1 and 4 are correct, and your answer to 5 is half correct.
2. d = ((vf + vi) / 2) t
To solve for t, divide both sides by what's in the parenthesis:
d / ((vf + vi) / 2) = t
If you wish, you can simplify:
t = 2d / (vf + vi)
3. d = vi t + ½ a t²
To solve for a, first subtract vi t from both sides:
d − vi t = ½ a t²
Multiply both sides by 2:
2d − 2 vi t = a t²
Divide by t²:
a = (2d − 2 vi t) / t²
To solve for t when vi = 0, first substitute 0 for vi:
d = (0) t + ½ a t²
d = ½ a t²
Multiply both sides by 2:
2d = a t²
Divide both sides by a:
t² = 2d / a
Take the square root:
t = √(2d / a)
5. Fg = G m₁ m₂ / r²
To solve for r, first multiply both sides by r²:
Fg r² = G m₁ m₂
Divide both sides by Fg:
r² = G m₁ m₂ / Fg
Take the square root;
r = √(G m₁ m₂ / Fg)
Your other answer is correct.
Overall, good effort!