Use this table of a school bus during morning pickups to calculate its average speed between 0 h and 2.340 h.
| Position (km) | Time (h) |
|---------------|----------|
| 0.0 | 0.000 |
| 1.2 | 0.024 |
| 2.8 | 0.051 |
| 4.2 | 0.084 |
| 16.3 | 2.340 |
Answer (1)
Calculate the total distance traveled: Δ x = 16.3 km − 0.0 km = 16.3 km .
Calculate the total time taken: Δ t = 2.340 h − 0.000 h = 2.340 h .
Calculate the average speed: v a vg = 2.340 h 16.3 km = 6.965811965811967 km/h .
The average speed of the school bus is 6.97 km/h .
Explanation
Understanding the Problem We are given a table showing the position of a school bus at different times. We need to calculate the average speed of the bus between time 0 h and 2.340 h.
Defining Average Speed The average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the total distance traveled is the difference between the final position and the initial position, and the total time taken is the difference between the final time and the initial time.
Calculating Distance and Time The initial position of the bus at time 0.000 h is 0.0 km. The final position of the bus at time 2.340 h is 16.3 km. Therefore, the total distance traveled is:
Δ x = 16.3 km − 0.0 km = 16.3 km
The initial time is 0.000 h and the final time is 2.340 h. Therefore, the total time taken is:
Δ t = 2.340 h − 0.000 h = 2.340 h
Calculating Average Speed Now, we can calculate the average speed by dividing the total distance traveled by the total time taken:
v a vg = Δ t Δ x = 2.340 h 16.3 km = 6.965811965811967 km/h
Rounding to three significant figures, the average speed is approximately 6.97 km/h.
Final Answer Therefore, the average speed of the school bus between 0 h and 2.340 h is approximately 6.97 km/h .
Examples
Understanding average speed is crucial in everyday scenarios, like planning a road trip. Imagine you're driving from one city to another, a distance of 350 km, and you want to know how long it will take. If you maintain an average speed of 70 km/h, you can calculate the estimated travel time by dividing the distance by the speed: 350 km / 70 km/h = 5 hours. This calculation helps you plan your journey, accounting for potential stops and traffic. Knowing average speed helps in time management and making informed decisions about travel.
