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Use the formula $s = ut + \frac{1}{2}at^2$ - OCR - GCSE Maths - Question 1 - 2017 - Paper 1

Question 1

$Use-the-formula-$s-=-ut-+-\frac{1}{2}at^2$-OCR-GCSE Maths-Question 1-2017-Paper 1.png$

Use the formula $s = ut + \frac{1}{2}at^2$. (a) Calculate $s$ when $u = 5$, $t = 10$ and $a = 3$. (b) Make $a$ the subject of the formula.

Worked Solution & Example Answer:Use the formula $s = ut + \frac{1}{2}at^2$ - OCR - GCSE Maths - Question 1 - 2017 - Paper 1

Step 1

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Answer

To calculate the distance $s$ , we can substitute the given values into the equation:

$s = ut + \frac{1}{2}at^2$

Substituting the values: $s = (5)(10) + \frac{1}{2}(3)(10^2)$

Calculating the first term: $s = 50 + \frac{1}{2}(3)(100)$

Calculating the second term: $s = 50 + \frac{300}{2}$

$s = 50 + 150$

Thus, the final value is: $s = 200$

Step 2

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Answer

Starting with the formula: $s = ut + \frac{1}{2}at^2$

To make $a$ the subject, we will isolate $a$ on one side. First, subtract $ut$ from both sides:

$s - ut = \frac{1}{2}at^2$

Next, multiply both sides by $2$ :

$2(s - ut) = at^2$

Finally, divide both sides by $t^2$ :

$a = \frac{2(s - ut)}{t^2}$

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