A racecar completes exactly 300 laps around a 0.5-km racetrack in 2 hours. What is the average velocity of the racecar? a 0 km/h b. 75 km/h c. 150 km/h d. 300 km/h
The correct answer and explanation is:
The correct answer is: a. 0 km/h
Explanation:
Average velocity is defined as the total displacement divided by the total time taken. Displacement refers to the straight-line distance from the starting point to the ending point, along with its direction. It is a vector quantity.
In this problem, the racecar completes exactly 300 laps around a 0.5-kilometer track. This means the car travels a total distance of:
300 laps × 0.5 km/lap = 150 km
However, since the car finishes exactly where it started after completing the 300 laps, the displacement is zero. The car’s initial position and final position are the same point on the track.
Total time taken is 2 hours.
To calculate average velocity, the formula is:
Average velocity = Displacement / Time
Substituting the values:
Average velocity = 0 km / 2 hours = 0 km/h
Even though the car traveled a total distance of 150 km, its displacement is zero, so the average velocity is zero.
It is important to differentiate average velocity from average speed. Average speed is the total distance traveled divided by the total time and is a scalar quantity without direction. In this case, the average speed would be:
Average speed = 150 km / 2 hours = 75 km/h
This matches option b, but since the question specifically asks for average velocity, the correct answer is zero.
In summary, because the racecar ends up back at the starting point after completing the laps, the displacement is zero. Dividing zero displacement by any time results in zero average velocity, regardless of the total distance covered or speed during the race.