A body is moved from rest along a staight line by a machine delivering constant power .Calcualte the velo0city and distance moved by the body as a funidion of time .

Options

A. S = `at+bt^(2)`, a, b are constants
B. S = `bt^(2) , b` is a constant
C. S = `at^(3//2),` a is constant
D. S = `at,a` is constant

Answer

C

Explanation

From the definition of power, we get
`P=(Delta KE)/(dt) = ((1)/(2) mv^(2) -0) )/( (t-0))= ((1)/(2) mv^(2) )/( t)`
As, engine is working at constant power.
Therefore, `v= ((2P)/(m) )^(1//2) sqrt(t)=K sqrt(t) " "["where", K= sqrt((2P)/( M)) = " constant ]`
`rArr (dx)/(dt) = K sqrt( t) rArr int_(0)^(S) dx= K int_(0)^(t ) sqrt(t) dt`
`rArr S=K (t^(3//2))/( (3//2)) rArr S= (2 K)/( 3) t^(3//2)`
`rArr S= "at"^(3//2)`, where, `a= (2K)/( 3)=` constant