The values for the average speed and average velocity are;
(a) [tex]Average \ speed = 1.37\overline{142857} \ m/s[/tex]
(b) [tex]The \ average \ velocity = 0.\overline{857142} \ m/s[/tex]
The reason the above values are correct is given as follows;
The given parameters are;
Distance of the nearest grocery store to the house, d = 60 m
Direction of the grocery store = East from the house
Walking speed, s = 1.2 m/s
Time of walking before the rain started, t₁ = 15.0 s
Time it takes to go back to the house, t₂ = 5.0 s
Speed at which the start walking again, s = 1.2 m/s
(a) The formula for average speed, [tex]s_{avg}[/tex], is given as follows;
[tex]s_{avg} = \dfrac{Total \ distance }{Sum \ of \ time \ taken}[/tex]
The distance walked before the rain, d₁ = 1.2 m/s × 15.0 s = 18 meters
Distance covered on returning to the house = d₂ = d₁ = 18 meters
The total distance covered, ∑Distance = d₁ + d₂ + 60
∴ ∑Distance = 18 m + 18 m + 60 m = 96 m
The time, t₃, it takes to get to the grocery store on the second attempt after getting the umbrella is given as follows;
[tex]t_3 = \dfrac{d}{v}[/tex]
[tex]t_3 = \dfrac{60 \ m}{1.2 \ m/s} = 50.0 \, s[/tex]
The total time, ∑Time = t₁ + t₂ + t₃
∴ ∑Time = 15.0 s + 5.0 s + 50.0 s = 70.0 s
[tex]Average \ speed = \dfrac{\sum Distance}{\sum Time}[/tex]
[tex]Average \ speed = \dfrac{96 \, m}{70 \, s} = \dfrac{48}{35} \ m/s= 1.37\overline{142857} \ m/s[/tex]
[tex]Average \ speed = 1.37\overline{142857} \ m/s[/tex]
(b) The average velocity, [tex]v_{avg}[/tex], is given as follows;
[tex]v_{avg}= \dfrac{Total \ displacement}{Total \ time}[/tex]
The total displacement = The total change in location = The change in location from the house to the grocery = 60 m
The total time is the same as for the average speed, ∑Time = 70 s
[tex]\therefore v_{avg}= \dfrac{60 \, m}{70 \, s} = \dfrac{6}{7} \ m/s = 0.\overline{857142} \ m/s[/tex]
[tex]The \ average \ velocity = 0.\overline{857142} \ m/s[/tex]
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