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 40 m. If he completes the 200 m dash in 26.4 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration (in m/s2) as he runs the curved portion of the track? m/s2 †

Answer 1

Answer:

$a_c=1.44\ m/s^2$

Explanation:

Centripetal Acceleration

It's the acceleration that an object has when traveling on a circular path to take into consideration the constant change of velocity it must have in order to keep going in the circular path.

Being v the tangent speed, and r the radius of curvature of the circle, then the centripetal acceleration is given by

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

We can compute the value of v by using the distance and the time taken to travel:

$\displaystyle v=\frac{x}{t}=\frac{200\ m}{26.4\ s}$

$v=7.58\ m/s$

Now we calculate the centripetal acceleration

$\displaystyle a_c=\frac{7.58^2}{40}=1.44\ m/s^2$

$\boxed{a_c=1.44\ m/s^2}$