A student wanted to drive from Austin to san Antonio ,80 mi south of Austin on highway I35. Unfortunately he entered in the wrong direction and drove to waco-100 miles north of Austin –before he noticed his error. In waco ,he turned around,drove back to Austin and continued to San Antonio . The whole trip took 5.46 h.
What was the student’s average speed during this trip? Answer in units of mph
What was the student’s average velocity during this trip? Take your positive direction to be southbound on I -35.
distance= 80+2*100=280
speed=distance/time
veloctiy= 80/time Southbound
Would the time southbound be if I were to half 5.46? Or, I looked it up that it would take about 1 h 30 min from austin to san antonio.
I ended up taking 80mi/1.5h=53mph.
If that's not a good way to go about it, how do I figure out the time southbound?
I also tried 180mi/51.3(t)=3.50877193h. Then i took 80mi/that answer to get 22.8mph. Is that the right approach?
To find the student's average speed during the trip, we can use the formula:
Average Speed = Total Distance / Total Time
1. First, let's calculate the total distance traveled by the student.
Distance from Austin to Waco = 100 miles (northbound)
Distance from Waco back to Austin = 100 miles (southbound)
Distance from Austin to San Antonio = 80 miles (southbound)
Total Distance = 100 miles + 100 miles + 80 miles = 280 miles
2. The question states that the total trip took 5.46 hours.
Now, we can calculate the average speed:
Average Speed = Total Distance / Total Time
= 280 miles / 5.46 hours
≈ 51.29 mph
Therefore, the student's average speed during the trip was approximately 51.29 mph.
To find the student's average velocity during the trip, we need to take into account the direction of motion. Since the positive direction is southbound on I-35, any northbound motion should be considered negative.
1. The student traveled from Austin to Waco, which is 100 miles north, so we consider this part of the trip as negative velocity.
2. The student traveled from Waco back to Austin, which is 100 miles south, so this part of the trip is positive velocity.
3. Finally, the student traveled from Austin to San Antonio, which is 80 miles south, so this part of the trip is also positive velocity.
To calculate the average velocity, we add the positive distances and subtract the negative distances, then divide by the total time.
Total Distance (positive) = 100 miles + 80 miles = 180 miles
Total Distance (negative) = 100 miles
Average Velocity = (Total Distance Positive - Total Distance Negative) / Total Time
= (180 miles - 100 miles) / 5.46 hours
≈ 15.03 mph
Therefore, the student's average velocity during the trip, considering the direction, was approximately 15.03 mph.