Answer: [tex]2.27\ m/s^2[/tex]
Explanation:
Given
Length of the race track [tex]L=200\ m[/tex]
the radius of curvature of the track [tex]r=29.5\ m[/tex]
time taken to run on track is [tex]t=24.4\ s[/tex]
Speed of runner is
[tex]\Rightarrow v=\dfrac{L}{t}=\dfrac{200}{24.4}\\\\\Rightarrow v=8.196\ m/s[/tex]
Centripetal acceleration is
[tex]\Rightarrow a_c=\dfrac{v^2}{r}=\dfrac{8.196^2}{29.5}\\\\\Rightarrow a_c=2.27\ m/s^2[/tex]
