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An object starting from rest slide on sl...

An object starting from rest slide on slope with `45^(@)`. If co-efficient of friction between object and surface is 0.3 x where x is distance covered then at what distance speed will be maximum ?

Text Solution

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Acceleration of object parallel to slope `a= g sin theta = mu g cos theta `
`v (dv )/( dx ) = g sin theta - mu g cos theta`
`:. , (d v)/( dx ) = ( g sin 45^(@) - 0.3 xg cos 45^(@))/( v )`
For define value of x when `(d v)/( dx ) = 0` then will be maximum
`:. , 0 = g - 0.3 kg`
`:. , 0.3x =1 rArr x = (1)/(0.3) = 3.33 m`
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