# Thread: How far in first minute?

1. ## How far in first minute?

hey guys, i think i might have to use dv/dt = -kv. i have no idea how do this problem, help me solve this

Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10sec later the boat has slowed down to 20 ft/s. Assume that the resistance it encouters while coasting is proportional to the squire of its velocity. how far does the motorboat coast in the first minute after its motor quits?

2. Originally Posted by DMDil
hey guys, i think i might have to use dv/dt = -kv. i have no idea how do this problem, help me solve this

Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10sec later the boat has slowed down to 20 ft/s. Assume that the resistance it encouters while coasting is proportional to the squire of its velocity. how far does the motorboat coast in the first minute after its motor quits?
I assume that's "square" ...

$\frac{dv}{dt} = -kv^2$

$\frac{dv}{v^2} = -k \, dt$

$-\frac{1}{v} = -kt + C$

$v = \frac{1}{kt+C}$

use your given speeds and times to find $k$ and $C$