Here is a speed-time graph for a train journey between two stations. The journey took 100 seconds. (a) Calculate the time taken by the train to travel half the distance between the two stations. You must show all your working. (b) Compare the acceleration of the train during the first part of its journey with the acceleration of the train during the last part of its journey.

GCSE Edexcel Maths Forming & Solving Equations: Here is a speed-time graph for a

Here is a speed-time graph for a train journey between two stations - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 2

Question 22

Here is a speed-time graph for a train journey between two stations. The journey took 100 seconds. (a) Calculate the time taken by the train to travel half the dist... show full transcript

Worked Solution & Example Answer:Here is a speed-time graph for a train journey between two stations - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 2

Step 1

Calculate the time taken by the train to travel half the distance between the two stations.

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Answer

To find the distance traveled during the journey, we calculate the area under the speed-time graph.

Calculate the area for the first part (0 to 60 seconds):
- The speed is constant at 12 m/s for 60 seconds.
- Area = Speed × Time = 12 m/s × 60 s = 720 m.
Calculate the area for the second part (60 to 100 seconds):
- The speed changes linearly from 12 m/s to 0 m/s.
- This forms a triangle.
- Base = 40 s (from 60 to 100 seconds), Height = 12 m/s.
- Area = (1/2) × Base × Height = 0.5 × 40 s × 12 m/s = 240 m.
Total distance = First part + Second part = 720 m + 240 m = 960 m.
Half the distance = 960 m / 2 = 480 m.

To find the time taken to travel 480 m:

During the first part (60 seconds), the train traveled 720 m. Hence, the entire journey's 480 m is fully accommodated within the first segment.
To find an exact point at which the 480 m occurs, we can calculate from the speed.

Using proportion:

Time for 480 m = (480 m / 12 m/s) = 40 seconds.
Thus, the answer for part (a) is 40 seconds.

Step 2

Compare the acceleration of the train during the first part of its journey with the acceleration of the train during the last part of its journey.

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Answer

In the first part of the journey (0 to 60 seconds), the train moves with a constant speed of 12 m/s, resulting in an acceleration of 0 m/s² since there is no change in speed.

In the last part of the journey (60 to 100 seconds), the train decelerates from 12 m/s to 0 m/s.

The initial speed is 12 m/s, and the final speed is 0 m/s over a duration of 40 seconds.
Thus, the acceleration can be calculated using the formula:

$a = \frac{v_f - v_i}{t} = \frac{0 - 12}{40} = -0.3 \text{ m/s}^2$

Therefore, the acceleration is negative during the last part, indicating deceleration, while the acceleration during the first part is 0 m/s².

Here is a speed-time graph for a train journey between two stations - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 2

Worked Solution & Example Answer:Here is a speed-time graph for a train journey between two stations - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 2

Calculate the time taken by the train to travel half the distance between the two stations.

Compare the acceleration of the train during the first part of its journey with the acceleration of the train during the last part of its journey.

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