Question

A typical running track is an oval with 74-m-diameter half circles at each end. A runner going once around the track covers a distance of 400m . Suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s.What is her centripetal acceleration during the turn at each end of the track?

Answer 1

Answer:

The acceleration towards the center will be $0.43\ m/s^2$

Explanation:

Given the running track is an oval shape, and the diameter of each half-circle is 74 meters.

Also, the runner took 1 minute and 40 seconds to complete 400 m one round of the track.

We need to find the acceleration towards the center.

First, we will find the speed.

$v=\frac{d}{t}$

Where $v$ is the speed.

$d$ is the distance covered by the rider that is 400 meters.

$t$ is the time taken by the rider to complete the lap which is 1 minute and 40 seconds.  $(60\ s +40\ s) = 100$ seconds.

So,

$v=\frac{400}{100}=4\ m/s$

And

$a_c=\frac{v^2}{r}$

Where $a_c$ is the acceleration towards the center.

$r$ is the radius which will be the half of the diameter 74 meters.

Hence, the radius will be 37 meters.

$a_c=\frac{4^2}{37} \\a_c=\frac{16}{37}=0.43\ m/s^2$

So, the centripetal acceleration of the rider will be $0.43\ m/s^2$