student wanted to drive from Austin to San

Antonio, 80 miles south of Austin on highway
I35. Unfortunately, he entered the highway in
the wrong direction and drove all the way 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 4.29 h.
What was the student’s average speed during this trip?
Answer in units of mph
011 (part 2 of 2) 10.0 points
What was the student’s average velocity
during his trip? Take your positive direction
to be southbound on I35.
Answer in units of mph

Well, isn't this student a real highway comedy show! Let's calculate their average speed first. They drove a total distance of 100 miles one way, and 80 miles the other way, so that's a total of 180 miles. And since the trip took 4.29 hours, we can divide the distance by the time to get the average speed: 180 miles / 4.29 hours = 42 miles per hour.

Now, let's talk about velocity. Remember, velocity includes direction. Since the positive direction is southbound on I35, and the student traveled a total distance of 180 miles, we would consider the displacement to be -180 miles (since they ended up 180 miles south of their starting point). Dividing the displacement by the total time, we get -180 miles / 4.29 hours = -42 miles per hour.

So, the average speed was 42 mph, but the average velocity was -42 mph. The student really took quite the detour!

To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken.

The student initially drove 100 miles in the wrong direction (north) to Waco and then drove back 100 miles to Austin. So, the total distance traveled during this part of the trip is 100 + 100 = 200 miles.

Then, the student continued driving from Austin to San Antonio, which is 80 miles south of Austin. So, the distance traveled during this part of the trip is 80 miles.

The total distance traveled is 200 + 80 = 280 miles.

The total time taken for the whole trip is 4.29 hours.

To find the average speed, we divide the total distance by the total time:

Average speed = Total distance / Total time
Average speed = 280 miles / 4.29 hours
Average speed ≈ 65.28 mph (rounded to two decimal places)

Therefore, the student's average speed during this trip was approximately 65.28 mph.

To find the average velocity, we need to consider the direction as well. Since the positive direction is southbound on I35, the student initially traveled north to Waco, so the velocity during that part is negative. Then, the student turned around and traveled south to San Antonio, so the velocity during that part is positive.

Since the total displacement is 80 miles south, the average velocity is simply the displacement divided by the total time:

Average velocity = Total displacement / Total time
Average velocity = 80 miles / 4.29 hours
Average velocity ≈ 18.63 mph (rounded to two decimal places)

Therefore, the student's average velocity during his trip was approximately 18.63 mph.

To find the student's average speed during the trip, we can divide the total distance traveled by the total time taken.

First, let's calculate the total distance traveled. The student initially drove from Austin to Waco, which is a distance of 100 miles. Then, the student turned around and drove back to Austin, covering the same 100 miles again. Finally, the student continued from Austin to San Antonio, which is a distance of 80 miles. So, the total distance traveled is 100 + 100 + 80 = 280 miles.

Next, let's calculate the total time taken for the trip, which is given as 4.29 hours.

Now, we can calculate the average speed using the formula:
Average Speed = Total Distance / Total Time

Average Speed = 280 miles / 4.29 hours

Calculating this, we find that the student's average speed during the trip was approximately 65.23 mph.

To find the student's average velocity during the trip, we need to consider the direction. The positive direction is southbound on I35, which is the direction from Austin to San Antonio.

Since the student initially traveled in the wrong direction, their velocity was negative during that portion of the trip. However, when they turned around and drove back to Austin, their velocity became positive again, and they continued in the positive direction towards San Antonio.

Therefore, the student's average velocity can simply be the displacement divided by the total time.

Displacement = Final Position - Initial Position
Displacement = 80 miles (San Antonio) - (-80 miles) (Austin)
Displacement = 160 miles

Average Velocity = Displacement / Total Time

Average Velocity = 160 miles / 4.29 hours

Calculating this, we find that the student's average velocity during the trip was approximately 37.28 mph (southbound on I35).