Abeba walks to school. She walks 1 km in 15 minutes. She meets her friend Makers - they talk for 5 minutes and then carry on walking to school. They walk 800 m in 10 minutes.
(a) draw a displacement-time graph to show Abeba's journey to school.
(b) what was the average velocity of Abeba's journey? Give your answer in m/s
(c) when was Abeba walking the fastest? Explain your answer.
(b) (1000 + 800) / (15 + 5 + 10) m/min
(c) compare 1000/15 and 800/10
(a) Sorry, I can't draw a graph as I am a text-based bot. But I can try to describe it to you!
Let's say the x-axis represents time in minutes, and the y-axis represents displacement in meters from her starting point.
For the first 15 minutes, Abeba walks 1 km, so her displacement is 1000 meters. So, at this point, her y-coordinate would be 1000.
Then, Abeba meets her friend Makers, and they talk for 5 minutes, so her displacement remains the same.
Afterward, they continue walking and cover a distance of 800 meters in 10 minutes. So, her displacement changes to 1800 meters.
(b) To find the average velocity, we divide the total displacement (1800m) by the total time (15 + 5 + 10 = 30 minutes). Thus, the average velocity is 1800m/30min = 60m/min (or meters per minute).
To convert it to m/s, we divide by 60 (since there are 60 seconds in a minute). So, the average velocity will be 60m/min ÷ 60 = 1m/s.
(c) Abeba was walking the fastest during the 10 minutes she covered 800m. This is because her speed is determined by the distance covered divided by the time taken. Among the three segments of her journey, she covered the most distance in the least amount of time during this 10-minute period, indicating the highest speed or fastest walking pace.
(a) To draw the displacement-time graph for Abeba's journey to school, we need to plot the distance covered by Abeba at different points in time.
First, Abeba walks 1 km in 15 minutes, which can be represented as a line with a slope of 1 km/15 min or 1000 m/900 s.
Next, Abeba and her friend Makers talk for 5 minutes. During this time, her position remains the same, so we draw a horizontal line on the graph.
After the conversation, they continue walking and cover a distance of 800 m in 10 minutes. This can be represented with a line segment with a slope of 800 m/600 s or 4/3 m/s.
Here's the displacement-time graph:
|
1 km /
\ /
\______/
5 min 10 min 15 min
(b) The average velocity is calculated by dividing the total displacement by the total time.
Since the total displacement is 1 km + 800 m = 1.8 km = 1800 m,
and the total time is 15 min + 5 min + 10 min = 30 min = 1800 s,
the average velocity is:
(1800 m)/(1800 s) = 1 m/s.
So, the average velocity of Abeba's journey is 1 m/s.
(c) Abeba was walking the fastest during the second phase when she covered a distance of 800 m in 10 minutes. This means her speed during this time period was 800 m / 600 s = 4/3 m/s.
During the first phase, she walked 1 km in 15 minutes, which is a speed of 1000 m / 900 s = 10/9 m/s.
Since 4/3 m/s is greater than 10/9 m/s, Abeba was walking fastest during the second phase, when she covered the 800 m distance.
To answer these questions, we'll need to use the given information about Abeba's journey. Let's break it down step by step:
(a) Draw a displacement-time graph:
On the x-axis, we'll represent time in minutes, and on the y-axis, we'll represent distance in kilometers. Let's plot the given information:
- From 0 to 15 minutes: Abeba walks 1 km.
- From 15 to 20 minutes: Abeba and Makers talk, so the distance remains the same.
- From 20 to 30 minutes: Abeba and Makers walk an additional 0.8 km.
The graph will show a straight line segment from (0,0) to (15,1), a flat line segment from (15,1) to (20,1), and another straight line segment from (20,1) to (30,1.8). This represents Abeba's journey to school.
(b) Calculate the average velocity:
Average velocity is defined as the total displacement divided by the total time taken. In this case, we have a change in displacement of 1.8 km (from 0 km to 1.8 km) and a total time of 30 minutes.
To convert the total time to seconds, we multiply it by 60:
Total time = 30 minutes = 30 × 60 = 1800 seconds
Average velocity = total displacement / total time
Average velocity = 1.8 km / 1800 s
To convert kilometers to meters, we multiply by 1000:
Average velocity = 1.8 km × 1000 / 1800 s
Average velocity = 1000 m / 1800 s
Simplifying this gives us the average velocity:
Average velocity = 0.5556 m/s (rounded to four decimal places)
(c) Determine when Abeba was walking the fastest:
To find when Abeba was walking the fastest, we need to look at the steepest part of the displacement-time graph. In this case, the steepest part is the straight line segment from (15,1) to (20,1). This segment represents Abeba and Makers talking, so Abeba's walking distance remained constant during this time.
Therefore, Abeba was walking the fastest during the time interval where she covers a distance of 0.8 km in 10 minutes. This is the straight line segment from (20,1) to (30,1.8) on the graph.
I hope this explanation helps! Let me know if you have any further questions.