Maximum Velocity of a Boat in a Race

In summary, 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. By writing the equations of motion for each phase and adding the expressions for the three distances which sum to 225m, the maximum velocity of the boat can be solved for.
  • #1
beatlemaniac
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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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  • #2
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.
 

What is the maximum velocity of a boat?

The maximum velocity of a boat depends on several factors such as the size and shape of the boat, the power of the engine, and the water conditions. Generally, a small boat with a powerful engine can reach speeds of up to 60 miles per hour, while larger boats may have a maximum velocity of 30-40 miles per hour.

How is the maximum velocity of a boat affected by water conditions?

Water conditions such as wind, waves, and currents can greatly impact the maximum velocity of a boat. For example, strong headwinds can slow down a boat's speed, while favorable currents can increase it. Additionally, rough seas can make it difficult for a boat to maintain its maximum velocity.

Can a boat exceed its maximum velocity?

Technically, yes, a boat can exceed its maximum velocity under certain conditions. However, this can put a strain on the boat's engine and may lead to mechanical issues. It is always recommended to operate a boat within its designated maximum velocity to ensure safety and longevity.

How is the maximum velocity of a boat measured?

The maximum velocity of a boat is typically measured in knots, which is a unit of speed equivalent to one nautical mile per hour. This is the standard unit used in the marine industry to measure the speed of boats and ships.

Can the maximum velocity of a boat be increased?

Yes, the maximum velocity of a boat can be increased through various means such as upgrading the engine, reducing the weight of the boat, or improving the hull design. However, it is important to note that increasing the maximum velocity may also require other safety measures to be taken into consideration.

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