GCSE OCR Maths Solving equations: 2 (a) Rearrange this formula t

2 (a) Rearrange this formula to make u the subject - OCR - GCSE Maths - Question 2 - 2023 - Paper 6

Question 2

2 (a) Rearrange this formula to make u the subject. $$v^2 = u^2 + 2as$$ (b) A rocket accelerates at 90 m/s² and travels 270 km. The rocket's final velocit... show full transcript

Worked Solution & Example Answer:2 (a) Rearrange this formula to make u the subject - OCR - GCSE Maths - Question 2 - 2023 - Paper 6

Step 1

Rearrange this formula to make u the subject

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Answer

To rearrange the formula $v^2 = u^2 + 2as$ to make u the subject, we start by isolating $u^2$ on one side:

Subtract $2as$ from both sides: $v^2 - 2as = u^2$
Take the square root of both sides: $u = ext{±} \\sqrt{v^2 - 2as}$ This expression gives us the value of u.

Step 2

Using part (a), or otherwise, calculate the rocket's initial velocity

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Answer

From part (a), we have the formula: $u = ext{±} \\sqrt{v^2 - 2as}$

Given:

Final velocity $v = 8000 \, m/s$
Acceleration $a = 90 \, m/s^2$
Distance $s = 270 \, km = 270000 \, m$

Now, substituting the values into the equation:

Calculate $2as$ : $2 imes 90 imes 270000 = 48600000$
Now substituting in the rearranged formula: $u = ext{±} \\sqrt{8000^2 - 48600000}$ $= ext{±} \\sqrt{64000000 - 48600000}$ $= ext{±} \\sqrt{15400000}$ $≈ 3932.0 \, m/s$

Since initial velocity cannot be negative, we choose the positive value: $u ≈ 3932.0 \, m/s$

2 (a) Rearrange this formula to make u the subject - OCR - GCSE Maths - Question 2 - 2023 - Paper 6

Worked Solution & Example Answer:2 (a) Rearrange this formula to make u the subject - OCR - GCSE Maths - Question 2 - 2023 - Paper 6

Rearrange this formula to make u the subject

Using part (a), or otherwise, calculate the rocket's initial velocity

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