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katrin [286]
3 years ago
10

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 †
Physics
1 answer:
nlexa [21]3 years ago
4 0

Answer:

a_c=1.44\ m/s^2

Explanation:

<u>Centripetal Acceleration</u>

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}

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