Photo AI
The graph shows the speed of a tram as it travels from the library to the town hall - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Question 8
The graph shows the speed of a tram as it travels from the library to the town hall. Speed (m/s) Not to scale. (a) Calculate the deceleration of the tram as it ap... show full transcript
Worked Solution & Example Answer:The graph shows the speed of a tram as it travels from the library to the town hall - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Step 1
Calculate the deceleration of the tram as it approaches the town hall.
Answer
To calculate the deceleration, we first identify the speed of the tram before it begins to decelerate, which is 6 m/s at 65 seconds, dropping to 0 m/s at 85 seconds. The change in speed is:
[ \Delta v = v_f - v_i = 0 - 6 = -6 \text{ m/s} ]
The time taken for this change is: [ \Delta t = 85 - 65 = 20 \text{ s} ]
Using the formula for acceleration (deceleration in this case):
[ a = \frac{\Delta v}{\Delta t} = \frac{-6}{20} = -0.3 \text{ m/s}^2 ]
Thus, the deceleration of the tram is -0.3 m/s².
Step 2
Calculate the distance travelled by the tram between the library and the town hall.
Answer
To find the distance, we can break the journey into two segments:
- From 0 to 65 seconds (constant speed of 6 m/s)
- From 65 to 85 seconds (decelerating from 6 m/s to 0 m/s)
Segment 1:
Distance = speed × time
[ d_1 = 6 \text{ m/s} \times 65 \text{ s} = 390 \text{ m} ]
Segment 2:
This portion is a triangle under the speed-time graph with a base of 20 s and a height of 6 m/s. The area of the triangle gives the distance.
[ d_2 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \text{ s} \times 6 \text{ m/s} = 60 \text{ m} ]
Total Distance:
[ d = d_1 + d_2 = 390 m + 60 m = 450 m ]
Step 3
What was the maximum speed of the tram as it travelled between the library and the town hall? Give your answer in kilometres per hour.
Answer
The maximum speed of the tram, as indicated by the graph, is 6 m/s. To convert this speed from meters per second to kilometers per hour, we use the conversion factor:
[ 1 \text{ m/s} = 3.6 \text{ km/h} ]
Thus,
[ 6 \text{ m/s} \times 3.6 = 21.6 \text{ km/h} ]
Therefore, the maximum speed of the tram as it travelled between the library and the town hall is 21.6 km/h.