Average Speed and Velocity Calculation in a Road Trip

What are the average speeds and average velocity for a road trip from San Antonio to Houston and back?

(a) What is the average speed from San Antonio to Houston?

(b) What is the average speed from Houston back to San Antonio?

(c) What is the average speed for the entire trip?

(d) What is the average velocity for the entire trip?

Answer:

Part a) Average speed from San Antonio to Houston is 61 km/h

Part b) Average speed from Houston back to San Antonio is 59.4 km/h

Part c) Average speed for the entire trip is 60.2 km/h

Part d) The average velocity for the entire trip must be ZERO

In this road trip scenario, the driver travels from San Antonio to Houston and back, covering equal distances at different speeds. The calculations for average speed and average velocity are based on the total round trip.

To calculate the average speed for each segment of the trip, we use the formula:

average speed = total distance / total time

For the first part of the trip, from San Antonio to Houston:

Half the distance is covered at 51 km/h and the other half at 71 km/h. By using the formula and the given speeds, the average speed for this segment is calculated to be 61 km/h.

For the second part of the trip, from Houston back to San Antonio:

Again, half the distance is covered at 51 km/h and the other half at 71 km/h. The average speed for this segment is calculated to be 59.4 km/h.

When we calculate the average speed for the entire trip:

Using the previous calculations and formula, the average speed for the entire trip is found to be 60.2 km/h.

For average velocity:

Since the total displacement of the entire trip is zero (starting and ending at the same point), the average velocity for the entire trip must be ZERO. This is because velocity is a vector quantity that takes into account direction, and with a round trip the net displacement is zero.