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# Make t the subject of the formula s = ut + ½ at²

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D

## DETAILS…

We’re going to be using the almighty formula to make t the subject of the formula s = ut + ½ at²:

Recall that a quadratic equation has the nature ax² + bx + c = 0

from the given problem, we have:

s = ut + ½ at²

Rearranging, we have:

0 = ½ at² + ut – s, or

½ at² + ut – s = 0

Multiplying through by 2, we then have:

at² + 2ut – 2s = 0

comparing this with ax² + bx + c = 0, we have:

a = a, b = 2u, c = -2s, and also take note that x = t

Applying this to the general solution for a quadratic equation using the almighty formula, we have:

### Now for the right answer to the above question:

1. Option A is incorrect. there should be a minus sign before u
2. Option B is incorrect. there should be a plus sign inside the square root.
3. C is incorrect. there should be a minus sign before u.
4. D is the correct answer.

## KEY-POINTS…

• The almighty formula is the general formula used to solve any quadratic equation.
• Please be careful when playing with signs, many students usually miss it at this point.

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