Can you help with velocity of a boat please.?

After switching off the engine of a speedy motorboat, the acceleration of the boat follows the equation, a=Kv3; K=constant. Show that , after t time from switching the engine off, the velocity of the boat is v=v01+2Ktv20, v0=initial velocity while switching the motor to the off position.

1 Answer
Apr 1, 2018

See below.

Explanation:

If a=.v=Kv3 then after multiplication by v in both sides we have

12ddtv2=Kv4 and making u=v2 we get

12ddtu=Ku2 This is a separable differential equation with solution

duu2+2Kdt=0u=12Kt+C0 and finally

u=v2v=12Kt+C0

now considering

v0=1C0 we have

v=v01+2Kv20t