Question

A 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 5 h. What was the student’s average speed during this trip? 1. 36 mph 2. 16 mph south 3. 56 mph north 4. 56 mph 5. Not enough information is given. 6. 16 mph 7. 36 mph south 013 (part 2 of 3) 10.0 points What was the student’s average velocity during his trip? 1. Not enough information is given. 2. 36 mph south 3. 16 mph 4. 36 mph 5. 56 mph 6. 56 mph north 7. 16 mph south 014 (part 3 of 3) 10.0 points What was the student’s average velocity from Austin to Waco? 1. 36 mph 2. 56 mph 3. 36 mph south 4. 16 mph 5. Not enough information is given. 6. 56 mph north 7. 16 mph south

Answer 1

Part 1. 4. 56 mi/h; Part 2. 7. 16 mi/h south; Part 3. 6. 56 mi/h north

Step-by-step explanation:

Part 1. Average speed

Speed = distance/time

Distance = Austin-Waco + Waco-Austin + Austin-San Antonio

= 100 mi + 100 mi + 80 mi = 280 mi

Time = 5 h

Speed = 280 mi/5 h = 56 mi/h

Part 2. Average velocity

Velocity is a vector. It includes both speed and direction.

Assume south is positive and north is negative.

Distance = -100 mi + 100 mi + 80 mi = +80 mi

Velocity = +80 mi/5h = +16 mi/h = 16 mi/h south

Part 3. Average velocity Austin-Waco

Distance = north

If the student kept to an average speed of 56 mi/h, the average velocity was 56 mi/h north.