Make u the subject of formula, E = $\frac{m}{2g}$(v2 - u2)

Analyze the question: We need to rearrange E = (m/2g)(v² − u²) so that u stands alone on one side.

Concept: Use inverse operations in reverse order: undo the multiplication, then the subtraction, then the square.

Solution:

1. Start with E = (m/2g)(v² − u²)

2. Multiply both sides by 2g: 2gE = m(v² − u²)

3. Divide both sides by m: 2gE/m = v² − u²

4. Make u² the subject by moving it to the left and 2gE/m to the right: u² = v² − 2gE/m

5. Take the square root of both sides: u = √(v² − 2Eg/m)

Checking the options:

• A: √(v² − 2Eg/m). This matches our result exactly.
• B: Has v²/m and 4 in the denominator, so it is wrong.
• C: Has v instead of v², so it is wrong.
• D: Has the wrong structure because it multiplies instead of subtracting, so it is wrong.

The correct answer is A.

Tip: In "change of subject" questions, remove the things attached to the variable in reverse order, as in BODMAS. Always remember to square root at the end, and check that v² keeps its square, as option C tries to trick you on this.