# Homework Help: Force and motion in Newton's laws

1. Oct 5, 2011

### theunloved

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

Attempted to solve:
Take upwards as positive for y direction, x + from left to right

From newton's law 2, we have:
-fk = ma
a = -fk/m = -70Vi / m

(Vi = V initial)

V = Vi + at
---------> t = (V - Vi) /a

t = - m(V - Vi) / 70Vi (h)
with m = 1000kg, V = 45km/h, Vi = 90 km/h

However, my answer is not correct from the book. Can someone point out where I did wrong ? Thanks

2. Oct 5, 2011

### DukeLuke

If the acceleration is based on the object's speed is it really constant?

3. Oct 5, 2011

### theunloved

Oh I got it, since acceleration is not constant, we can't use all the kinematic equations to solve this problem.....But how are we gonna find acceleration if we only have one equation ?