Question

1. 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 30 m. if he completes the 200 m dash in 23.2 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration as he runs the curved portion of the track?

Explanation:

Step1: Calculate the speed of the runner

The runner runs a distance $d = 200$ m in time $t=23.2$ s. The speed $v$ is given by the formula $v=\frac{d}{t}$. So, $v=\frac{200}{23.2}\text{ m/s}$.

Step2: Calculate the centripetal acceleration

The formula for centripetal acceleration $a_c$ is $a_c=\frac{v^{2}}{r}$, where $r = 30$ m is the radius of curvature. First, we find $v=\frac{200}{23.2}\approx8.62$ m/s. Then $a_c=\frac{(8.62)^{2}}{30}$.
$a_c=\frac{74.3}{30}\approx2.48$ m/s²

Answer:

$2.48$ m/s²