Answer:
The distance by which the child is safe is [tex]k = 10 \ m[/tex]
Explanation:
From the question we are told that
The speed of the motorcycle is [tex]v_n = 30 m/s[/tex]
The distance of the child from the motorcycle is L = 190 m
The reaction time is [tex]t_r = 1 \ s[/tex]
deceleration is [tex]a = -3m/s^2[/tex]
Generally the distance covered during the reaction time is
[tex]D = v_n * t_r[/tex]
=>[tex]D = 30 * 1[/tex]
=> [tex]D = 30 \ m[/tex]
Generally the distance covered during the deceleration
[tex]v^2 = u^2 + 2as[/tex]
Here v is the final velocity which is zero
So
[tex]0 = 30 ^2 + 2 * (-3)s[/tex]
=> [tex]s = 150 \ m[/tex]
So the total distance the motorcycle rider will cover before coming to rest is
[tex]d = D + s[/tex]
=> [tex]d = 30 + 150[/tex]
=> [tex]d = 180 \ m[/tex]
Therefore the amount of distance by which the child id safe is
[tex]k = L -d[/tex]
=> [tex]k = 190 -180[/tex]
=> [tex]k = 10 \ m[/tex]
