Someone verify if this is correct, please!
1. Draw a distance versus time graph that corresponds to the walk described below.
Adam starts 8 m away from the motion sensor and walks in a straight line toward the sensor at a constant rate of 0.5 m/s for 3 s. He immediately begins walking away from the sensor at a constant rate of 0.25 m/s for 4s. He stops for 1s and then walks toward the sensor at a constant rate of 0.5 m/s for 2 s.
Image is here imgur dot com/aKwAy
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2.
During what interval of time was the greatest distance travelled?
a) 0<t<5
b) 5<t<7
c) 7<t<10
d) cannot be determined
I don't which one is correct, 0<t<5 or 5<t<7
here is the image:
imgur dot com/vOojV
Thank yhou~
For (1), the x-coordinates are plotted correctly. You will need to review the y-coordinates, because they do not seem to correspond with the ones given in the question.
The starting point of 8 m is correct.
Walking towards the sensor makes a line with negative slope is correct also.
The rate is 0.5m/sec., so over 3 seconds, he would have been closer by 3*0.5=1.5m.
So at the end of 3 seconds, he would be at a distance of 8-1.5=6.5 m from the sensor.
Proceed this way for the rest of the question and see if you arrive at 6.5 m at the end of the 10 seconds.
(2) You'd need to interpret the graph where the y-axis represents speed given by m/s.
Interval, speed
0-5 3m/s
5-7 4m/s
7-10 1m/s
Since distance = speed * time, you can calculate the distance covered in each interval and the interval with the greatest distance travelled is the right answer.
Got it! THank you~~~~~~~
Great! You're welcome!
To verify if the given distance versus time graph is correct, we can break down the walk described and calculate the distances covered at different time intervals.
First, let's analyze the motion described:
1. Adam starts 8m away from the motion sensor and walks towards it at a constant rate of 0.5m/s for 3 seconds.
- Distance covered = Speed × Time = 0.5m/s × 3s = 1.5m
- The graph should show a linear increase in distance from 8m to 9.5m.
2. Adam immediately begins walking away from the sensor at a constant rate of 0.25m/s for 4 seconds.
- Distance covered = Speed × Time = 0.25m/s × 4s = 1m
- The graph should show a linear decrease in distance from 9.5m to 8.5m.
3. Adam stops for 1 second and then walks towards the sensor at a constant rate of 0.5m/s for 2 seconds.
- Distance covered = Speed × Time = 0.5m/s × 2s = 1m
- The graph should show a linear increase in distance from 8.5m to 9.5m.
Based on these calculations, the correct graph should start at 8m, increase to 9.5m, decrease to 8.5m, and finally increase back to 9.5m.
Now let's address the second question regarding the greatest distance traveled. Looking at the given graph, we can observe that the highest point corresponds to the highest distance traveled.
The options provided are:
a) 0 < t < 5
b) 5 < t < 7
c) 7 < t < 10
d) Cannot be determined
By analyzing the graph, the highest point occurs during the time interval 5 < t < 7, where the distance reaches closer to 10m. Therefore, option b) 5 < t < 7 is the correct answer.
Now that the answers have been verified, you can be confident that the distance versus time graph is correct, and the interval of greatest distance traveled is 5 < t < 7.