What is the magnitude of the acceleration of a sprinter running at 9.0 m/s when rounding a turn of a radius 26 m?
The acceleration of an object in circular motion
= v²/r
where
r=radius
v = tangential velocity
9^2
--- = 3.115
26
To find the magnitude of the acceleration of the sprinter, we need to use the equation for centripetal acceleration, which is given by:
a = v^2 / r
where:
a is the magnitude of acceleration
v is the velocity of the sprinter
r is the radius of the turn
In this case, the velocity of the sprinter is 9.0 m/s, and the radius of the turn is 26 m. Plugging these values into the equation, we can calculate the magnitude of the acceleration:
a = (9.0 m/s)^2 / 26 m
Simplifying the equation, we get:
a = 81 m^2/s^2 / 26 m
To calculate the final value, we divide 81 m^2/s^2 by 26 m:
a ≈ 3.115 m/s^2
Therefore, the magnitude of the acceleration of the sprinter rounding the turn is approximately 3.115 m/s^2.