Maximum Velocity of a Boat in a Race

AI Thread Summary
The discussion focuses on calculating the maximum velocity of a boat during a race, which involves three phases of motion: initial acceleration, constant velocity, and deceleration to rest. The boat starts at 3 m/s, accelerates uniformly for 10 seconds, maintains a constant speed for 6 seconds, and then decelerates over 6 seconds, covering a total distance of 225 meters. To solve the problem, one must write equations of motion for each phase and sum the distances to equal 225 meters. The user expresses difficulty in approaching the problem and seeks guidance on how to proceed with the calculations. The solution requires setting up and solving the equations derived from the motion phases.
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Homework Statement



A boat starts a race at 3 m/s, accelerates uniformly for 10 seconds, then travels with constant velocity for 6 seconds. It then slows uniformly to rest in another 6 seconds. If the boat has traveled a total distance of 225m, find the maximum velocity.

Homework Equations



a(t) = v`(t) = s``(t)

The Attempt at a Solution



Obviously the boat has three phases of motion:
- the initial acceleration
- the constant velocity
- and the negative acceleration until it comes to rest

And I need to find the constant velocity. However I am honestly stuck I do not even know how to approach this question! Please help!
 
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The analysis is OK.
Now you need to write the equations of motion for each one of the three phases.
Add the expressions for the three distances and this will be 225 m.
Solve the equation to find the speed.
 
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