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A runner taking part in the 200-m dash must run around the end of a track that has a circular arc with a radius of curvature of 29.5 m. The runner starts the race at a constant speed. If she completes the 200-m dash in 24.4 s and runs at constant speed throughout the race, what is her centripetal acceleration as she runs the curved portion of the track

Respuesta :

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]

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