Maximum Velocity of a Boat in a Race

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SUMMARY

The discussion focuses on calculating the maximum velocity of a boat during a race, which involves three distinct 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 velocity for 6 seconds, and then decelerates uniformly over 6 seconds, covering a total distance of 225 meters. To find the maximum velocity, one must derive the equations of motion for each phase and sum the distances to equal 225 meters.

PREREQUISITES
  • Understanding of kinematic equations of motion
  • Knowledge of uniform acceleration and deceleration concepts
  • Ability to solve equations involving distance, velocity, and time
  • Familiarity with basic physics principles related to motion
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion
  • Learn how to derive equations for motion in multiple phases
  • Practice solving problems involving distance, velocity, and time relationships
  • Explore graphical representations of motion to visualize acceleration and deceleration
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This discussion is beneficial for physics students, educators, and anyone interested in understanding motion dynamics, particularly in the context of real-world applications like racing scenarios.

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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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