A point moves rectilinearly with deceleration whose modulus depends on the velocity v of the particle as `w=asqrtv`, where a is a positive constant. At the initial moment the velocity of the point is equal to `v_0`. What distance will it traverse before it stops? What time will it take to cover that distance?

Explanation

According to the problem
`-(vdv)/(ds)=asqrtv` (as v decrease with time)
or, `-underset(v_0)overset0intsqrtvdv=aunderset0overset(s)intds`
On integrating we get `s=(2)/(3a)v_0^(3//2)`
Again according to the problem
`-(dv)/(dt)=asqrtv` or `-(dv)/(sqrtv)=adt`
or, `underset(v_0)overset(0)int(dv)/(sqrtv)=a underset0 oversett intdt`
Thus `t=(2sqrt(v_0))/(a)`