The graph shows the velocity of a particle over the first 20 minutes of its motion. Velocity (m/min) v 0 15 20 Not to scale Between 7 minutes and 15 minutes the velocity of the particle is v metres per minute. The average velocity of the particle over the 20 minutes is 11.55 metres per minute. Find the value of v. You must show your working.

GCSE OCR Maths Averages: The graph shows the velocity of

The graph shows the velocity of a particle over the first 20 minutes of its motion - OCR - GCSE Maths - Question 19 - 2023 - Paper 4

Question 19

The graph shows the velocity of a particle over the first 20 minutes of its motion. Velocity (m/min) v 0 15 20 Not to scale Between 7 minutes and 15 minutes th... show full transcript

Worked Solution & Example Answer:The graph shows the velocity of a particle over the first 20 minutes of its motion - OCR - GCSE Maths - Question 19 - 2023 - Paper 4

Step 1

Find the total distance over 20 minutes

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Answer

The average velocity of the particle is given by the formula:

$ext{Average Velocity} = \frac{\text{Total Distance}}{\text{Total Time}}$

Given that the average velocity is 11.55 m/min over 20 minutes, we can find the total distance:

$\text{Total Distance} = \text{Average Velocity} \times \text{Total Time} = 11.55 \times 20 = 231 \text{ metres}$

Step 2

Calculate the distance for each time interval

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Answer

From the graph, we break down the motion into three intervals:

From 0 to 7 minutes, the particle moves with a velocity of 15 m/min:
- Distance = Velocity × Time = 15 × 7 = 105 metres.
From 7 to 15 minutes, the velocity is v m/min:
- Distance = Velocity × Time = v × (15 - 7) = 8v metres.
From 15 to 20 minutes, the particle moves with a velocity of 0 m/min:
- Distance = Velocity × Time = 0 × 5 = 0 metres.

Step 3

Set up the equation based on total distance

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Answer

The total distance covered in 20 minutes is the sum of distances from each interval:

$\text{Total Distance} = 105 + 8v + 0 = 231$

Thus, we can set up the equation:

$105 + 8v = 231$

Step 4

Solve for v

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Answer

Now, we can solve for v:

$8v = 231 - 105$ $8v = 126$ $v = \frac{126}{8} = 15.75$

Therefore, the value of v is 15.75 m/min.

The graph shows the velocity of a particle over the first 20 minutes of its motion - OCR - GCSE Maths - Question 19 - 2023 - Paper 4

Worked Solution & Example Answer:The graph shows the velocity of a particle over the first 20 minutes of its motion - OCR - GCSE Maths - Question 19 - 2023 - Paper 4

Find the total distance over 20 minutes

Calculate the distance for each time interval

Set up the equation based on total distance

Solve for v

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