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Q.

The deceleration experienced by a moving motorboat, after its engine is cut-off is given by dvdt=-kv3 where k is constant. If vo is the magnitude of velocity at cut-off, the magnitude of velocity at time 't' after the cut-off is:

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a

v02

b

vo

c

voe-kt

d

vo2v02kt+1

answer is D.

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Detailed Solution

dvdt=−kv3⇒∫vovv−3 dv=∫0tk dt⇒v−2−2vov=−kt⇒−121v2−1v02=−kt⇒1v2=1v02+2kt⇒v=vo2v02kt+1
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