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A particle having a velocity $u = u_{0}$ at $t = 0$ is decelerated at the rate $| a | = α \sqrt{v}$ , where $α$ is a positive constant.

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The particle comes to rest at t=2v0α

The particle will come to rest at infinity

The distance travelled by the particle before coming to rest is 2v03/2α

The distance travelled by the particle before coming to rest is 2ν03/23α

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detailed solution

Correct option is A

(1) a=-αv∴dvdt=-αvor ∫01dt=-1α∫v00v-1/2·dv∴t= 2v0α(4)a=-αv∴v.dvds=-αv∴∫0sds=-1α∫v00v1/2dv∴s=2v03/23α

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A particle having a velocity u=u0 at t=0 is decelerated at the rate |a|=αv, where α is a positive constant.

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Ready to Test Your Skills?

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A particle having a velocity $u = u_{0}$ at $t = 0$ is decelerated at the rate $| a | = α \sqrt{v}$ , where $α$ is a positive constant.