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 30.0 m. The runner starts the race at a constant speed. If she completes the 200-m dash in 23.2 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

The centripetal acceleration of the runner is 2.48 m/s²

Step-by-step explanation:

Given :

Distance covered by runner, d = 200 m

Time taken by runner to complete 200 m , t = 23.2 s

Radius of the circular arc, r = 30 m

Consider v be the constant speed of the runner.

The constant speed is determine by the relation:

`v=(d)/(t)`

`v=(200)/(23.2)`

v = 8.62 m/s

Consider
`a_(c)` be the centripetal acceleration.

The relation to determine centripetal acceleration is:

`a_(c)=(v^(2) )/(r)`

`a_(c)=((8.62)^(2) )/(39)`

`a_(c)=2.48 \ m/s^(2)`