1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A boat's acceleration is proportional to its velocity

  1. Sep 25, 2005 #1
    A 1000kg boat is traveling at 90km/h when its engine is shut off. The magnitude of the frictional force f between the boat and water is proportional to the speed v of the boat: f=70v where v is in meters per second and f is in newtons. Find the time required for the boat to slow to 45 km/h.

    This problem wasn't assigned so I might be trying something I'm not supposed to know how to do. I have a FBD and have defined the x-axis in the direction of the boat's motion.

    -f=ma=-70v
    therefore v(t)=[tex]-\int .070vdt [/tex]

    I wish I could show more work but I'm don't know where to go next. I think this employs some calculus I'm not familiar with so if someone could just point out a concept I need to look at I would appreciate it.
     
  2. jcsd
  3. Sep 25, 2005 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Write a=(dv/dt).
    So, you have (dv/dt)=-kv, where k is a constant.

    This is a "differential equation for v".
    To solve for v, you have to find a function v that satisfies this equation. You don't need a class in differential equations to solve this, however.

    Can you think of a function of t whose derivative is proportional [with a negative constant] to itself? If you can't you can try a technique called "separation of variables" to obtain such a function.
     
  4. Sep 25, 2005 #3
    Thanks I got it.
     
  5. Jan 28, 2010 #4
    To keep the problem real use drag force proportional to the velocity squared as:

    Water Drag = 1/2 xCd x A x V^2 or proportional to V^2 with Cd and A constant.

    Same functional relation for air drag except different Cd and A
     
    Last edited: Jan 28, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A boat's acceleration is proportional to its velocity
  1. A accelerating boat (Replies: 2)

  2. Boat velocity (Replies: 5)

Loading...