Answer:
The total time is: t=451.22 sec
The average speed is: V=34.57 m/s
Explanation:
Average speed
The average speed is calculated by dividing the total distance traveled by an object (x) by the total time it took it to travel that distance (t).
[tex]\displaystyle V=\frac{x}{t}[/tex]
Since the student makes the trip in two parts, we have to calculate the total distance and the total time.
We know the distance to school is 7.8 Km = 7,800 m. The student makes his way home over the same distance, thus the total distance is
x=2*7,800 m=15,600 m
The first trip to school was done at an average speed of v1=32.6 m/s. Knowing the distance and speed, we can calculate the time:
[tex]\displaystyle t1=\frac{x1}{v1}=\frac{7,800}{32.6}=239.26\ sec[/tex]
The second trip back home was done at an average speed of v2=36.8 m/s. Let's calculate the second time:
[tex]\displaystyle t2=\frac{x2}{v2}=\frac{7,800}{36.8}=211.96\ sec[/tex]
The total time is:
[tex]t=239.26\ sec+211.96\ sec=451.22\ sec[/tex]
[tex]\boxed{t=451.22\ sec}[/tex]
The average speed is:
[tex]\displaystyle V=\frac{15,600}{451.22}=34.57\ m/s[/tex]
[tex]\boxed{\displaystyle V=34.57\ m/s}[/tex]
