- #1
sanhuy
- 40
- 2
Homework Statement
A 500 kg boat moves with an initial speed of 20 m/s turns off it engine and slows down due to the drag force. If this force has magnitude F= 15.3v^2 find the boat speed after 12 seconds.
Homework Equations
∑F = ma
dv = adt
The Attempt at a Solution
taking the side opposite to the drag force to be positive in our force equation we get:
-15.3v2 = m(-a) = m(-dv/dt).
so,
∫-15.3/500 dt = ∫ (1/v^2) dv with the correct limits i get V = -3.4m/s which is incorrect.
however, when i use the force equation
-15.3v2 = m(a) = m(dv/dt) { no negative sign for dv/dt} i get the right answer v = 2.4 m/s .
I don't understand why this works. isn't acceleration in the same direction as the net drag force, so by how i set up my coordinate system they both should have a negative sign? Please help me understand. i looked online and in my textbook and i found nothing.