abeba walks to school. she walks 1 km in 15 minutes. she meets her friend makeda - they talk for 5 minutes and then carry on walking to school. they walk 800 m in 10 minutes. a) draw adisplacement - 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.
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a) To draw a displacement-time graph for Abeba's journey to school, we will plot her position on the y-axis (displacement) and time on the x-axis.
First, we consider Abeba's initial position as 0 km at the starting time. At 15 minutes, she walks 1 km. So, we plot a point (1, 15) on the graph.
Next, she meets her friend Makeda and talks for 5 minutes, so her position remains constant at 1 km for those 5 minutes. Thus, we draw a horizontal line from (1, 15) to (1, 20).
After that, Abeba continues walking with her friend and covers a distance of 800 m in 10 minutes. We convert 800 m to km (800 m ÷ 1000 = 0.8 km) and plot the point (1.8, 30) on the graph.
The graph will show a straight line from (1, 15) to (1, 20), and then from (1, 20) to (1.8, 30).
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Time (minutes)
b) To calculate the average velocity, we need to find the total displacement and divide it by the total time.
Total displacement = 1.8 km - 0 km = 1.8 km
Total time = 30 minutes
Average velocity = Total displacement / Total time
Average velocity = 1.8 km / 30 minutes
Average velocity ≈ 0.06 km/min
To convert km/min to m/s, we know that 1 km = 1000 m and 1 min = 60 s.
Average velocity ≈ 0.06 km/min * (1000 m/1 km) * (1 min/60 s)
Average velocity ≈ 1 m/s
Therefore, the average velocity of Abeba's journey is 1 m/s.
c) Abeba was walking the fastest when she covered 800 m in 10 minutes. In this 10-minute interval, her velocity was constant, so she maintained a steady speed.
a) To draw a displacement-time graph for Abeba's journey to school, we can plot the time (in minutes) on the x-axis and the displacement (in meters) on the y-axis.
First, Abeba walks 1 km in 15 minutes. Since 1 km is equal to 1000 meters, we can plot a point at (15, 1000) on the graph.
Next, Abeba meets her friend Makeda and they talk for 5 minutes. During this time, she doesn't walk, so her displacement remains constant. We can represent this on the graph by drawing a horizontal line from (15, 1000) to (20, 1000).
Finally, Abeba and Makeda continue walking to school and cover a distance of 800 meters in 10 minutes. Plot another point at (30, 1800) on the graph.
Connecting the points, we get a straight line from (15, 1000) to (30, 1800). This line represents Abeba's journey to school.
b) To find the average velocity of Abeba's journey, we need to divide the total displacement by the total time taken.
The total displacement is 1800 meters (final position - initial position) and the total time is 30 minutes.
Average velocity = total displacement / total time
Average velocity = 1800 meters / 30 minutes
Average velocity = 60 meters per minute
To convert meters per minute to meters per second, divide by 60 (since there are 60 seconds in a minute):
Average velocity = 60 meters per minute / 60
Average velocity = 1 meter per second (m/s)
Therefore, the average velocity of Abeba's journey to school is 1 m/s.
c) Abeba was walking the fastest during the time she covered the greatest distance in the shortest amount of time. From the graph, we can see that Abeba covered a distance of 800 meters in 10 minutes. This means her velocity during this time was:
Velocity = Distance / Time
Velocity = 800 meters / 10 minutes
Velocity = 80 meters per minute
To convert meters per minute to meters per second, divide by 60:
Velocity = 80 meters per minute / 60
Velocity = 1.33 meters per second (m/s)
Therefore, Abeba was walking the fastest when she covered a distance of 800 meters in 10 minutes, with a velocity of approximately 1.33 m/s.