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?

The centripetal acceleration of the runner is 2.48 m/s²

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 = 8.62 m/s

Consider be the centripetal acceleration.

The relation to determine centripetal acceleration is:

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.