How Long Does It Take for a Boat to Decelerate from 90 km/h to 45 km/h?

[vaishakh]

A 1000kg boat is traveling at 90km/h when its engine is shut off. The magnitude of frictional force acting between the boat and the water is proportional to the speed of the boat and is given by 70vwhere the speed of the boat in meters per second is v. find the time required for the boat to slow down to the speed of 45 km/h.

I don't know how to start with this problem. Somebody here please give me a hint to solve this problem?

 

[bigplanet401]

Go straight to the Second Law:
$$F = ma = m\dot{v} \, .$$
The resistive force is proportional to the velocity, and acts opposite the boat's motion . You should draw the free-body diagram for this to make sure you get the signs right, or else you will end up with an answer that makes no sense!
Did you end up with a first-order differential equation in $$v$$? Solve for $$v(t)$$, and plug in the numbers.

 

[mezarashi]

Acceleration is not constant. Welcome to calculus-based physics.

Express the acceleration as a function of velocity, then apply the relationship:

$$a = \frac{dv}{dt}$$

Separate the variables and integrate. DO NOT forget to add your constant of integration. You will find that it is your initial velocity.