Question

7.

Answer 1

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;

$Average \ speed = \dfrac{Total \ Distance}{Total \ Time}$

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;

$The \ average \ speed = \dfrac{Total \ Distance}{Total \ Time} = \dfrac{6 \ miles }{1.5 \ Hours} = 4 \ miles \ per \ hour$

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;

$The \ average \ velocity = \dfrac{Final \ location - Initial \ location}{Time \ taken \ for \ the \ change \ in \ location}$

$The \ average \ velocity = \dfrac{Total \ displacement}{Time \ taken \ for \ the \ change \ in \ location}$

$The \ average \ velocity = \dfrac{Total \ change \ in \ location}{Time \ taken \ for \ the \ change \ in \ location}$

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;

$The \ average \ velocity = \dfrac{Sum \ total \ of \ change \ in \ location}{Time \ taken \ for \ the \ change \ in \ location} = \dfrac{3 + (-3) }{1.5}$

$The \ average \ velocity = \dfrac{3 \ miles + (-3) \ miles }{1.5} = \dfrac{0 \ miles }{1.5} = 0 \ mi/hr$

The average velocity = 0 mi/hr.