can you graph this for me?
In heavy rush-hour traffic you drive in a straight line at 12
m/s
for 1.5 minutes, then you have to stop for 3.5 minutes, and finally you drive at 15
m/s
for another 2.5 minutes. A
Plot a position-versus-time graph for this motion. Your plot should extend from
t=0
to
t=7.5
minutes.
Assume
x=0
and
t=0
at the start of your motion.
To graph the position-versus-time graph for this motion, we need to break it down into three parts: the initial drive at 12 m/s, the stop, and the final drive at 15 m/s.
Step 1: Define the time intervals.
We have three time intervals: the first drive for 1.5 minutes, the stop for 3.5 minutes, and the final drive for 2.5 minutes.
Step 2: Calculate the distances traveled.
Using the formula distance = speed × time, we can calculate the distances traveled in each interval:
- In the first interval, distance = 12 m/s × 1.5 minutes.
- In the second interval, we are stopped, so the distance is 0.
- In the third interval, distance = 15 m/s × 2.5 minutes.
Step 3: Plotting the graph.
Start by drawing the x-axis (representing time) and the y-axis (representing position). Mark the intervals on the x-axis and the corresponding distances on the y-axis.
- For the first interval (drive at 12 m/s), the distance traveled is the slope of the line, which is constant. Since the time is 1.5 minutes, plot a point at (1.5, distance traveled in the first interval).
- For the second interval (stop for 3.5 minutes), the distance traveled is 0. This means the position will remain the same during this interval. Plot a horizontal line at the same position as the previous point. This line should be horizontal for 3.5 minutes.
- For the third interval (drive at 15 m/s), the distance traveled is again the slope of the line. Since the time is 2.5 minutes, plot another point at (7.5, distance traveled in the third interval).
Now, you should have three points on the graph: (1.5, distance in the first interval), (5, the same distance as the point before the stop), and (7.5, distance in the third interval). Connect these points using straight lines.
Remember to label your axes and provide a title for your graph indicating it is a position-versus-time graph.
I hope this explanation helps you graph the motion correctly.