How Do You Calculate a Boat's Acceleration on a Circular Path?

AI Thread Summary
To calculate a boat's acceleration on a circular path with a radius of 20m, the total acceleration is determined by combining tangential acceleration and centripetal acceleration. The tangential acceleration (a(t)) is given as 2 m/s², while the centripetal acceleration (a(n)) is calculated using the formula v²/p, resulting in 1.25 m/s². By applying the formula a = (a(t)² + a(n)²)^(1/2), the magnitude of the boat's total acceleration is found to be approximately 2.36 m/s². The calculations seem accurate based on the provided values. This approach effectively combines both components of acceleration for a boat moving in a circular path.
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Homework Statement


A boat is traveling along a circular path having a radius of 20m. Determine the magnitude of the boat's acceleration when the speed is v=5m/s and the rate of increase in the speed is v'=2 m/s^2

Homework Equations



a=(a(t)^2+a(n)^2)^1/2

The Attempt at a Solution



I believe the a(t)=2 <--- May be wrong
and the equation for a(n)=v^2 / p which i got 1.25
so i pluged these into the relevant equation to get 2.36 m/s^2 is the magnitude of the boats acceleration
 
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my question is if i did it right or not
 
joemama69 said:
I believe the a(t)=2 <--- May be wrong
and the equation for a(n)=v^2 / p which i got 1.25
so i pluged these into the relevant equation to get 2.36 m/s^2 is the magnitude of the boats acceleration
Sounds good to me.
 

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