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**1. Homework Statement**

The acceleration of a particle is defined by the relation

a=-k(v)^2 k is a constant.

The particle starts at x=0 with a velocity of 20 m/s. At x=100 m its velocity is 15 m/s

Determine the distance traveled by the particle (starting from x=0)

A) before its velocity drops to 10 m/s

B)before it comes to rest.

This is the only problem in college I encountered that I couldn't solve. I took calculus 3 it seems to be so simple yet I have no idea how to solve. I dont get how I can find the position without the time traveled. I dont get how acceleration can be dependent on the velocity. I spent so many hours tryying to solve this. It seems like i could integrate a twice to obtain the position function but that turns out to be wrong. I cant believe that math class seems so easy to me but i cant even solve the math problems in a standard first year physics class. This seems to be a differential equations problem but it can't be as its in a first year physics class. Sorry i couldnt really attempt a solution because i dont know where to begin. Any help will be greatly appreciated.

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**