Question

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

Answer 1

Answer: $2.27\ m/s^2$

Explanation:

Given

Length of the race track $L=200\ m$

the radius of curvature of the track $r=29.5\ m$

time taken to run on track is $t=24.4\ s$

Speed of runner is

$\Rightarrow v=\dfrac{L}{t}=\dfrac{200}{24.4}\\\\\Rightarrow v=8.196\ m/s$

Centripetal acceleration is

$\Rightarrow a_c=\dfrac{v^2}{r}=\dfrac{8.196^2}{29.5}\\\\\Rightarrow a_c=2.27\ m/s^2$