1.

An object , moving with a speed of6.25 m//s , is decelerated at a rate given by : (dv)/(dt) = - 2.5 sqrt (v) where v is the instantaneous speed . The time taken by the object , to come to rest , would be :

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Solution :`(dv)/(dt) =-2.5 SQRT(V)`
`int_(6.25)^(0) v^(-1//2)dv = int_(0)^(t) 2.5 dt `
`[(v^(1//2))/(1//2)]_(6.25)^(0)=2.5 [t]_(0)^(t)`
`2[0-sqrt(6.25)]= -2.5 (t-0)`
`2[-2.5]= -2.5t`
`t=2s`


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