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Me:
Solve for t following equation: x = x₀ + v₀t + ½at²
ChatGPT2 / 2:
To solve for “t” in the equation x = x₀ + v₀t + ½at², where x, x₀, v₀, a are known values, we can rearrange the equation and solve for “t” using the quadratic formula.
The equation can be rearranged as follows:
½at² + v₀t + (x₀ – x) = 0
This is a quadratic equation in the form of at² + bt + c = 0, where: a = ½a b = v₀ c = x₀ – x
Now we can use the quadratic formula to solve for “t”:
t = (-b ± √(b² – 4ac)) / (2a)
Substituting the values, we get:
t = (-v₀ ± √(v₀² – 4(½a)(x₀ – x))) / (2(½a))
Simplifying further:
t = (-v₀ ± √(v₀² – 2a(x₀ – x))) / a
Therefore, the solution for “t” is given by:
t = (-v₀ ± √(v₀² – 2a(x₀ – x))) / a