Question

A particle starts with velocity v0​ at at time t=0 and is decelerated at a rate proportional to the square root of its speed  at time t with constant of proportionality α.The total time for which it will move before coming to rest is

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Answer 1

The particle comes to rest at t=2v√0α

The particle will come to rest at infinity

The distance travelled by the particle before coming to rest is 2v3/20α

The distance travelled by the particle before coming to rest is 2v3/203α

Answer :

A::D

Solution :

(a) a=−αv√

∴dvdt=−αv√

or ∫t0dt=−1α∫0v0v−1/2.dv

∴t=(2v√0)

(d) a=−αv√

∴v.dvds=−αv√

∴∫s0ds=−1α∫0v0v1/2dv

∴s=2v3/203α