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A commuting student leaves home and drives to school at an average speed of 39.0 km/h. After 23.0 min he realizes that he has forgotten his homework and returns home to get it at the same average speed. It takes 10.0 min to find the report, after which the trip to school 39.0 km away to the east is resumed at the same speed as before. What is the average speed for the entire trip ? What is the average velocity for the entire trip?

2 Answers

4 votes

Final answer:

The average speed for the entire trip is 83.6 km/h. The average velocity for the entire trip is zero.

Step-by-step explanation:

The average speed for the entire trip can be calculated by finding the total distance traveled divided by the total time taken. In this case, the student traveled 39.0 km to school and then returned the same distance back home, resulting in a total distance of 78.0 km. The total time taken for the entire trip is the sum of the time taken to drive to school, the time taken to return home, and the time spent finding the report, which is 23.0 min + 23.0 min + 10.0 min = 56.0 min. To convert the total time to hours, divide by 60: 56.0 min / 60 = 0.933 hours. Therefore, the average speed for the entire trip is 78.0 km / 0.933 hours = 83.6 km/h.

The average velocity for the entire trip can be determined by considering both the magnitude and direction of the displacement. In this case, since the student drove in the same direction to school and back home, the displacement is zero, meaning there was no change in position. Thus, the average velocity for the entire trip is also zero.

User Marceau
by
4.9k points
3 votes

Answer:
s_(avg)=(117)/((213)/(60))=32.95 km/h


v_(avg)=(39)/((213)/(60))=10.98 km/h

Step-by-step explanation:

Given

Distance between home and school is 39 km

Total time taken
=(39)/(39)+(23)/(60)+(39)/(39)+(10)/(60)+(39)/(39)

i.e.


t=3* 60+23+10=213 min

Total Distance traveled =39+39+39=117 km

displacement=39 km

Thus Average speed
=(Distance)/(Time\ taken)


s_(avg)=(117)/((213)/(60))=32.95 km/h

Average velocity
=(Displacemet)/(Time\ taken)


v_(avg)=(39* 60)/(213)=10.98 km/h

User Shelper
by
5.3k points