An ant crawls in a straight line at a constant speed of 0.35 m/s, beginning in the corner of a square classroom that is 5.00 m on a side. It first crosses the diagonal of the room and then turns to the right, continuing at 0.45 m/s to the far corner of the same wall from which it began. What was the ant's average speed for the whole trip?
A) 0.40 m/s
B) 0.16 m/s
C) 0.24 m/s
D) 0.39 m/s

Question

Quizplus · Accepted Answer

To find the average speed, we need to use the formula:
average speed = total distance / total time

First, let's calculate the total distance. The ant first crosses the diagonal of the room, which has a length of:

diagonal = 5.00 m x √2 ≈ 7.07 m

Then, the ant continues to crawl along one of the walls, which has a length of 5.00 m. So, the total distance is:

total distance = diagonal + wall = 7.07 m + 5.00 m = 12.07 m

Next, we need to calculate the total time. For this, we can use the formula:

time = distance / speed

The time taken by the ant to cross the diagonal is:

time1 = diagonal / speed1 = 7.07 m / 0.35 m/s ≈ 20.20 s

The time taken by the ant to crawl along the wall is:

time2 = wall / speed2 = 5.00 m / 0.45 m/s ≈ 11.11 s

So, the total time is:

total time = time1 + time2 ≈ 31.31 s

Finally, we can calculate the average speed as:

average speed = total distance / total time ≈ 12.07 m / 31.31 s ≈ 0.39 m/s

Therefore, the best choice is D.

An Ant Crawls in a Straight Line at a Constant