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Q.

The retardation experienced by a moving motor boat, after its engine is cut-off, is given by dvdt=-kv3 where k is a constant. If v0 is the magnitude of the velocity at cut-off, the magnitude of the velocity at time t after the cut-off is

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a

v0

b

v02

c

v0e-kt

d

v02v02kt+1

answer is D.

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Detailed Solution

As, dvdt=-kv3 ⇒∫v0vdvv3=-k∫0tdt ⇒-1k∫v0vv-3dv=t or -1kv-3+1-3+1v0v=t or 12k1v2-1v02=t or 1v2-1v02=2kt or 1v2=1v02+2kt or 1v2=1+2v02ktv02 or v=v02v02kt+1

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The retardation experienced by a moving motor boat, after its engine is cut-off, is given by dvdt=-kv3 where k is a constant. If v0 is the magnitude of the velocity at cut-off, the magnitude of the velocity at time t after the cut-off is