1) The two groups are side-by-side after 7 seconds
2) Distance covered by the adults: 28 m
Step-by-step explanation:
1)
The position of the kids at time t can be written as
[tex]x_k(t) = d + v_k t[/tex]
where
d = 21 m is the initial position of the kids with respect to the adults
[tex]v_k=1 m/s[/tex] is the speed of the kids
The position of the adults at time t instead can be written as
[tex]x_a(t)=v_a t[/tex]
where
[tex]v_a=4 m/s[/tex] is the speed of the adults
The two groups are side-by-side when the adults reach the same position of the kids, therefore:
[tex]x_k(t)=x_a(t)[/tex]
And solving for t, we find the time at which this happens:
[tex]d+v_k t = v_a t\\t=\frac{d}{v_a-v_k}=\frac{21}{4-1}=7 s[/tex]
2)
The distance covered by the adults during this time can be found by using the equation
[tex]x_a(t) = v_a t[/tex]
where
[tex]v_a[/tex] is the speed of the adults
t is the time
In this problem, we have
[tex]v_a=4 m/s[/tex] (speed)
t = 7 s (time at which the adults catch the kids)
Therefore, the distance covered is
[tex]x_a(7)=(4)(7)=28 m[/tex]
Learn more about speed:
brainly.com/question/8893949
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