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

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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 velocity is... 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 for uu, we start with the equation:
v2=u2+2asv^2 = u^2 + 2as.

  1. Subtract 2as2as from both sides:
    v2−2as=u2v^2 - 2as = u^2.
  2. Take the square root of both sides to isolate uu:
    u=ext±v2−2asu = ext{±} \sqrt{v^2 - 2as}.
    This gives us the rearranged formula for uu.

Step 2

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

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Answer

Given the information:

  • Final velocity v=8000 extm/sv = 8000 \, ext{m/s}
  • Acceleration a=90 extm/s2a = 90 \, ext{m/s}^2
  • Distance s=270 extkm=270000 extms = 270 \, ext{km} = 270000 \, ext{m}

Using the rearranged formula from part (a):
u=v2−2asu = \sqrt{v^2 - 2as}
Substituting the known values:
u=80002−2⋅90⋅270000u = \sqrt{8000^2 - 2 \cdot 90 \cdot 270000}
Calculating 800028000^2:
=64000000= 64000000
Calculating 2⋅90⋅2700002 \cdot 90 \cdot 270000:
=48600000= 48600000
Therefore:
u=64000000−48600000=15400000u = \sqrt{64000000 - 48600000} = \sqrt{15400000}
Finally:
u≈3924.3 extm/su \approx 3924.3 \, ext{m/s}.

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