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A car is travelling along a straight horizontal road with initial velocity $u$ ms$^{-1}$ - AQA - A-Level Maths Pure - Question 12 - 2022 - Paper 2

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A car is travelling along a straight horizontal road with initial velocity $u$ ms$^{-1}$. The car begins to accelerate at a constant rate $a$ ms$^{-2}$ for 5 second... show full transcript

Worked Solution & Example Answer:A car is travelling along a straight horizontal road with initial velocity $u$ ms$^{-1}$ - AQA - A-Level Maths Pure - Question 12 - 2022 - Paper 2

Step 1

Using the Equation of Motion

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Answer

To find acceleration, we can use the first equation of motion:

v=u+atv = u + at

Where:

  • vv is the final velocity (4u4u ms1^{-1})
  • uu is the initial velocity (uu ms1^{-1})
  • aa is the acceleration (what we need to find)
  • tt is the time (5 seconds)

Substituting the known values into the equation leads to:

4u=u+a54u = u + a \cdot 5

Step 2

Rearranging the Equation

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Answer

Now, rearranging the equation to solve for aa:

4uu=5a4u - u = 5a
3u=5a3u = 5a

To isolate aa, we divide both sides by 5:

a=3u5a = \frac{3u}{5}

Step 3

Expressing in Terms of u

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Answer

The expression can be simplified:

a=0.6ua = 0.6u

Thus, the correct answer is a=0.6ua = 0.6u. Remember to circle this answer.

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