Respuesta :
Answer:
a. The average speed is 4 mi/hr
b. The average velocity is 0 mi/hr
Explanation:
a. The average speed is given by the following formula;
[tex]Average \ speed = \dfrac{Total \ Distance}{Total \ Time}[/tex]
The given information are;
The time it took for one friend to run to his friend's house = 30 minutes
The distance between the two houses = 3 miles
The time it took for the friend to walk home = 1 hour
Therefore, the distance the friend ran going to his friend's house = 3 miles and the distance the friend walked going back his house = 3 miles
The total distance travelled = 3 + 3 = 6 miles
The total time taken = 1 hour + 30 minutes = 1 hour 30 minutes = 1.5 hours
Therefore;
[tex]The \ average \ speed = \dfrac{Total \ Distance}{Total \ Time} = \dfrac{6 \ miles }{1.5 \ Hours} = 4 \ miles \ per \ hour[/tex]
The average speed for the entire trip = 4 mi/hr
b. The average velocity is the total change in position divided by the total time taken to make the change or total displacement divided by the total time for the displacement
Mathematically, average velocity is given as follows;
[tex]The \ average \ velocity = \dfrac{Final \ location - Initial \ location}{Time \ taken \ for \ the \ change \ in \ location}[/tex]
[tex]The \ average \ velocity = \dfrac{Total \ displacement}{Time \ taken \ for \ the \ change \ in \ location}[/tex]
[tex]The \ average \ velocity = \dfrac{Total \ change \ in \ location}{Time \ taken \ for \ the \ change \ in \ location}[/tex]
Given that the friend changed his location to his friend's house, a distance of 3 miles he we have;
Initial change in location of the friend = 3 miles
After which the friend then relocates back to his house (and we know that it is the same journey but in opposite direction, he we have;
Final change in location of the friend = -3 miles
We are given that he ran to his friend's house and walked back home in a total time of 1 hour + 30 minutes = 1.5 hours, therefore, we have;
[tex]The \ average \ velocity = \dfrac{Sum \ total \ of \ change \ in \ location}{Time \ taken \ for \ the \ change \ in \ location} = \dfrac{3 + (-3) }{1.5}[/tex]
[tex]The \ average \ velocity = \dfrac{3 \ miles + (-3) \ miles }{1.5} = \dfrac{0 \ miles }{1.5} = 0 \ mi/hr[/tex]
The average velocity = 0 mi/hr.
