Question

a particle initially moving with a velocity u is subjected to a regarding force as a result of which it decelated at a rate a=-k√v when v is the instanous velocity and k is a positive constant the time t taken by the particles to come to rest is given by
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Answer 1

Answer:

The particle comes to rest at t=2v√0αt=2v0α

The particle will come to rest at infinity

The distance travelled by the particle before coming to rest is 2v3/20α2v03/2α

The distance travelled by the particle before coming to rest is 2v3/203α2v03/23α

Answer :

A::D

Solution :

(a) a=−αv√a=-αv

∴dvdt=−αv√∴dvdt=-αv

or ∫t0dt=−1α∫0v0v−1/2.dv∫0tdt=-1α∫v00v-1/2.dv

∴t=(2v√0)∴t=(2v0)

(d) a=−αv√a=-αv

∴v.dvds=−αv√∴v.dvds=-αv

∴∫s0ds=−1α∫0v0v1/2dv∴∫0sds=-1α∫v00v1/2dv

∴s=2v3/203α

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