1.

The decelerationof a cartravelingon astraighthighwayisafunctionof itsinstantaneousvelocityv givenbyomega= a sqrt (v)whereaisa constant. If theinitialvelocityofthe caris 60km/h , thedistanceof thecar willtraveland thetimeittakesbeforeit stopesare

Answer»

`2/3 m,1/2 s`
`3/( 2a)m, (1) /( 2a) s`
`(3a)/(2) m, ( a) /(2)s`
`(2)/(3a)m,2/ a s`

Solution :Deceleration` omega=- asqrt(v)`
But` omega= ( DV)/(dt)implies(dv )/(dt)=- a sqrt(v)`
` (-dv ) /( sqrt(v))= a. dtimpliesint _(v_f)^(0)( dv) /(sqrt(v))= inta dt `
` | 2 sqrt(v ) |_(v_f)^(0)-a timplies(dv) /( DX). ( dx) /( dt =- a sqrt(v) `
`( dv )/( dx ). v =- asqrt(v) impliesdv impliesdv sqrt(v)=- a . dx `
` INT _(v_0)^(0) sqrt(v)dv =- aint _(0)^(s )ds `
After solving, we get
` s=(2)//(3a) . V_(0^(3/2))`


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