SOLUTION: Make T the subject of the formula 1/2gt^2=s

Question 1083011: Make T the subject of the formula
1/2gt^2=s
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
start with 1/2 * g * t^2 = s

multiply both sides of the equation by 2 to get:

g * t^2 = 2 * s

divide both sides of the equation by g to get:

t^2 = (2 * s) / g

take the square root of both sides of the equation to get:

t = plus or minus sqrt( 2 * s) / g )

how do you know you did this correctly?

let's take the last equation and allow s to be equal to 4 and g to be equal to 2.

the last equation would become t = plus or minus sqrt( 2 * 4) / 2)

this would result in t = plus or minus sqrt( 4 ) which would result in t = plus or minus 2.

now that we know that t = plus or minus 2 because we solved for it using the final equation, and s = 4 and g = 2 because we made them that way, let's look at the original equation and replace the variables with their respective values.

the original equation is 1/2 * g * t^2 = s

when g = 2 and s = 4, this equation becomes:

1/2 * 2 * t^2 = 4

if we make t = plus 2, this equation becomes 1/2 * 2 * (2)^2 = 4 which becomes 1/2 * 2 * 4 = 4 which becomes 1/2 * 8 = 4 which becomes 4 = 4 which is true.

if we make t = minus 2, this equation becomes 1/2 * 2 * (-2)^2 = 4 which becomes 1/2 * 2 * 4 = 4 which becomes 1/2 * 8 = 4 which becomes 4 = 4 which is also true.

since the original equation is true after we replace t with the values that we solved for in the final equation, we can be reasonably sure that the solution is correct.

therefore:

the original equation is 1/2 * g * t^2 = s

the final equation is t = plus or minus sqrt( 2 * s / g )

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