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 †

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

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

Now we calculate the centripetal acceleration

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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